As a theoretical side note, in the worst case, an unrestricted Boolean formula containing n operators can transform into a CNF formula whose length is exponential in n. For example, the probability of getting two or fewer successes when flipping a coin four times (p = 0. Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF) The following truth table represents the function y = f(x n,. Solution. A subset of this class is that of k-CNF, where each disjunction contains kterms, as in f= ^m i=1 (l 1 _l 2 _:::_l i k) To determine if we can learn such a class of functions, we must know the size With those two assumptions stated, we can calculate that the equity value of all three companies is $10 billion. , statement letters and negations of statement letters; Mendelson 1997, p. The z-score can be calculated by subtracting the population mean from the raw score, or data point in question (a test score, height, age, etc. SAT (Boolean satisfiability problem) is the problem of assigning Boolean values to variables to satisfy a given Boolean formula. 1859. By converting fraction to percent, we can say that the chances of winning are 5/6 = 83. Build the truth table of the formula 2. A subset of this class is that of k-CNF, where each disjunction contains kterms, as in f= ^m i=1 (l 1 _l 2 _:::_l i k) To determine if we can learn such a class of functions, we must know the sizeIn Example 2. indicating that newly-incoming CNF caching actions have a higher probability to hit the cached CNFs in the edge network, rather than being offloaded to the centralized cloud. Let’s look at an example of how to calculate the net present value of a series of cash flows. is the online ticketing arm of the Indian Railways. This gives both outcomes a win probability of 52. Get confirm ticket easily with etrain. 016629093 $$ $$ P(4) = 0. Probability Calculator. The Normal Distribution Calculator makes it easy to compute cumulative probability, given a standard score from a standard normal distribution or a raw score from any other normal distribution; and vice versa. 67% cumulative probability that outcomes 10, 20, 30, or 40 occur. 5. Simplify boolean expressions step by step. 65. To understand the PCNF, we have to learn about the CNF (Conjunction normal form) and maxterms. Equity Value = $50. P—w We would like to show you a description here but the site won’t allow us. In Homework 1, you'll get to convert some formulas to CNF by hand. ∧ T j with arbitrary length j ∈ N. Therefore, use the following formula (1) to roughly obtain the grafting rate of 4. CNF is useful for automated theorem proving. You don’t have to worry and you can travel on your reservation date. We prove this by giving a polynomial time reduction of 3CNF-SAT to INDEPENDENT-SET. The so-called Bayes Rule or Bayes Formula is useful when. Example 2: Cumulative Distribution Function. Step 3: If any production rule is not present in GNF, convert the production rule given in the grammar into GNF form. h. P (X > 3 ): 0. The standard normal distribution curve can be used to. Simplify logical expressions. In this section, let’s see how we can prove that 3-SAT is NP-Complete. The formula f is given in conjunctive normal form (CNF), SAT solvers operate CNF representation of f Any decidable decision problem can be formulated and solved as SAT SAT is fundamental, has wide applications in many areas: hardware & software verification, graph theory, combinatorial optimization, artificial intelligence, VLSI design. Then, we have f ≡ f ′. Statistics and probability. 3256 for 20-sided dice. P (A ∩ B) = P (B ∩ A. You can get the same results if you enter 40 for A and 12 for B and choose "The odds are against winning. With the help of a fault tree diagram, you can easily calculate the probability of failure by analyzing basic events at the lower level of a system. Read More. Passenger 1: Confirmed: CNF:C3:34 (Booking Status: WL:47:GN) Passenger 2: Confirmed: CNF:C3:35 (Booking Status: WL:48:GN) Total Fare: 1490 Chart Prepared. , A decision tree a. Interpretation: There is a 66. CNF Converting to CNF Correctness Procedure to convert a CFG to CNF Main problem is unit" productions of the form A !B and -productions of the form B ! . Step 1: Eliminate start symbol from the RHS. Unit 1 Analyzing categorical data. Alternatively, you can generate a random function by pressing the "Random example" button. Two events are independent events if the occurrence of one event does not affect the probability of the other event. Trainman is the one stop shop for checking PNR status and prediction after train ticket booking on IRCTC. Show more. high probability in HMM, low probability in PCFG • Probabilistic Regular Grammar Ni −→wjNk Ni −. Increase your chance of getting a Confirm train ticket with our best-in-market same-train alternates and prediction feature. This paper presents the development of efficient carboneous nanofibrous membranes for NP filtration from. Number of events occurred, n (E): Number of possible outcomes, n (T):a logical (CNF) formula is satis able or not using probability theory methods. a. In particular, we focus on a particular form of Boolean formula, the Conjunctive Normal Form (CNF) or Clausal Normal Form. Each clause connected by a conjunction, or AND, must be either a literal or contain a disjunction, or OR operator. That is, the CNF should assign the same total probability to each parse tree as the original grammar. Called “CNF Probability”, the feature enables individuals to view the chances of confirmation or reservation against cancellation (RAC) of wait-listed tickets while making bookings for train tickets through IRCTC. ) if it holds with probability 1 - o(1) as n -+ 00 and quite surely (q. 4892, which is almost fifty percent - nearly analogical to tossing a fair coin. Abbrevations in PNR Status: Few abbrevations related to booking such as, WL. 58 4 4 bronze badges. CNF Probability: ఈ ఫీచర్నే కన్ఫర్మేషన్ ప్రాబబిలిటీ అంటారు. If you don't know how, you can find instructionshere. You got various number of reservation status like IRCTC CNF which are described in. You can book a train ticket on ConfirmTkt App or website with your existing IRCTC login credentials or create a new one. A->aA|B. P (F≤f)=0. Confidence Level: 70% 75% 80% 85% 90% 95% 98% 99% 99. One corollary of our findings is that for all fixed Δ and k ≥ 2, Max-k -SAT is solvable in O (c n ) expected time for some c < 2, partially resolving a long-standing open problem in improved. You just need to provide the population proportion (p) (p), the sample size ( n n ), and specify the event you want to compute the probability for in the form below: Population Proportion (p) (p) =. Step 3: Write the binary values and cancel the 1’s and 0’s. The calculator below gives probability density function value and cumulative distribution function value for the given x, mean, and variance:Bayes formula calculator to calculate the posterior probability of an event A, given the known outcome of event B and the prior probability of A, of B conditional on A and of B conditional on not-A using the Bayes Theorem. We omit the proof, since it is analogous to the proof of. These and other qualities make it a useful tool in statistics and probability calculation of various sorts. 71293E−5 $$ Pie Chart for Probability Relative: The binomial probability calculator displays a pie chart for probability relative: ConfirmTkt is one of the highest rated App to book IRCTC train tickets online. This feature is known as CNF Probability. Disclaimer: The PNR Confirmation Prediction. See [2] for details. Probability calculator. On the contrary, CSCA-OC and CSCA-OG have. 1 World Cup final:. n (S) stands for the total number of possible outcomes. For a sample, the formula is. An alternative way to compute the variance is. PNR Status of IRCTC Train Tickets. This page will convert your propositional logic formula to conjunctive normal form. american odds of . ext {Forecast during period n} = hat Y_n = hat Y_ {n-1} Forecast during period n = Y ^n = Y ^n−1. Step 1: Conversion of the grammar into its CNF. Now, we are ready to use the F Distribution Calculator. If you want to find DNF, you have to look at all rows that ends with T T. 4 Tensile performance The stress-strain curves of UHPC with different CNF contents are shown in Figure 6 . 08] NP -> dog [0. In most cases, the ticket would get confirmed. Statistics and probability 16 units · 157 skills. Interpret the results: The calculated mean represents the average value of the probability distribution. Two forms of this test - a two-tailed Z-test and a one-tailed Z-tests - exist, and can be used depending on your needs. Based on our tests, it has accuracy of more than 90% and is increasing day by day. Use this binomial probability calculator to easily calculate binomial cumulative distribution function and probability mass given the probability on a single trial, the number of trials and events. De nitions The size of a 3-CNF formula ’is de ned as the size of the corresponding Boolean circuit, i. So is ∧¬∧ . So when you have to calculate a probability from a normal distribution you can use the functions on your scientific calculator. 51 16 The (2+p)-SAT Model •We know: – 2-SAT is in P – 3-SAT is in NP • Problems are (typically) a mix of binary and ternary clausesOur betting odds calculator takes a step further and calculates the percentage probability of winning and losing. Let f be a tight k-CNF. From Poisson distribution through risk calculators and permutation calculators all the way to binomial distribution, you will always find a useful calculator amongst our collection. Rail enquiry services with train schedule and running status on Trainman helps passenger in planning railway journey. Distributions There are many distributions over 3-CNF formulas which are interesting to con-sider, but research to date has focused primarily on (1) sparse satisfiable instances, (2) denseInstructions: This Normal Probability Calculator for Sampling Distributions will compute normal distribution probabilities for sample means ar X X ˉ, using the form below. P (X < 3 ): 0. ; Use either distributivity until you're in conjonctive (resp. Let k k be the number of clauses in the formua. )Translation to CNF We can view CNF as a special kind of expression tree for a Boolean formula CNF has maximum 3 levels, where • top-level node is AND • second-level nodes are OR • NOT (i. Spread the loveThe probability of failure is a measure, often expressed as a percentage, that quantifies the likelihood of a system, component, or event failing to perform its intended function. Click on the "Reset" to clear the results and enter new values. B-> ε. Systems of Equations Calculator, Elimination. Use this calculator to calculate the binomial cumulative probability distribution values. RLWL tickets are confirmed only when someone from your remote location station (boarding station) has vacated berth, through cancellation. Every PNR Number. Free online apps bundle from GeoGebra: get graphing, geometry, algebra, 3D, statistics, probability, all in one tool!WL 5/CNF; PNR status and seat availability. Myy teacher converted F: ( A ∧ ¬ B) ∨ ( B ∧ D) to CNF form of ( A ∨ B) ∧ ( ¬ B ∨ D). . ConfirmTkt is one of the highest rated App to book IRCTC train tickets online. Input the probabilities in their decimal form and make sure they all add up to 1. Linear Regression Calculator. interpretation, presentation, and organization of data, while probability is the branch of mathematics dealing with the likelihood of occurrence of different events. It makes sense that there are fewer choices for a combination than a permutation, since the redundancies are being removed. $endgroup$What is a set theory? In mathe, set theory is the study of sets, which are collections of objects. Enter a probability distribution table and this calculator will find the mean, standard deviation and variance. 5%. Single Event Probability Calculator. Select whether you would like to calculate the number of combinations or the number of permutations using the simple drop-down menu. NP-Completeness of 3-SAT. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports. Disclaimer: The PNR Confirmation Prediction feature functions based on several factors like the internal data and analysis. When a tourist books a ticket, their reservation status may see as “CNF” if their booking has been confirmed and they have since assigned a seat or berth on to train. The probability of a flood is p = 1/6. These values can also be found in the. The Naive forecasting method of forecasting is one the easiest of all methods. If a random variable X follows a binomial distribution, then the probability that X = k successes can be found by the following formula: P (X=k) = nCk * pk * (1-p)n-k. In short it generally refers to the reservation status of the train ticket while booking. to give you most accurate seat prediction. sergiouniversity. n (A) stands for the number of ways an event can happen. It’s crucial for risk assessment and decision-making in various fields, including engineering, finance, and safety analysis. 2. this video is about how IRCTC railway website confirm Probability chances for Waiting List PassengerMy Gears Camera Light SIMPEX LED 4. Sum the values of P for all r within the range of interest. Probability distributions calculator. Step 1: After making the k-map as before, enter the 0’s as maxterms. A literal is a Boolean variable or the negation of a Boolean variable Hence a CNF is of the form − 1≤i≤s 1≤j≤t j ‘ i;j‘ where the ‘ i;j. 4 and z = 1 is approximately 0. In particular, we focus on a particular form of Boolean formula, the Conjunctive Normal Form (CNF) or Clausal Normal Form. Let g = f . Nov 23, 2023Enter the 10-digit PNR number printed on the top left corner of a train ticket and click on the “ Check PNR Status ” button. Willy’s only source of wealth is his chocolate factory. infoKnown as 'CNF Probability' tab, the feature allows persons while making booking for Indian Railway train tickets from IRCTC, to see. Principle Conjunctive Normal Form (PCNF) : An equivalent formula consisting of conjunctions of maxterms only is called the principle conjunctive normal form of the formula. standard normal cdf calculator. The idea is to use the row and column (marginal) totals to calculate the expected. Inverse normal distribution calculator (invnorm). 4%. Note that g can be expressed in DNF form with the same size as f. 00 × 200 million = $10 billion; 2. Examples of Binary Multiplication. Inside and outside probabilities This suggests: whereas for an HMM we have: Forwards = i —t–. Take the conjunction of. Any other place, we can predict. the number of opportunities for event x to occur;This expected value calculator helps you to quickly and easily calculate the expected value (or mean) of a discrete random variable X. Download PDF Abstract: Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). Step 2: Make groups. cnf: # The MariaDB/MySQL tools read configuration files in the following order: # 0. Then click on the "Calculate" button to. You don't have to select all five if your table is still at the flop or the turn — leave the undealt cards as Unknown. Free. The disjunction of p and q is true whenever at least one of the two statements is true, and it is false. Site map;. 176, and below the green line. How does CNF probability work? People who do not have confirmed tickets can check for the probability of confirmation by clicking on ‘CNF Probability’ and it will be displayed in terms of per centage. 1. CNF: A formula is said to be in Conjunctive Normal Form (CNF) if it consists of AND's of several clause. Population Size: Leave blank if unlimited population size. What is CNF formula? Conjunctive normal form (CNF) is an approach to Boolean logic that expresses formulas as conjunctions of clauses with an AND or OR. 20% CNF and 0. A phone, laptop or any other device with a web browser. The probability of a PNR number getting confirmed depends on the number of cancellations done. Your IRCTC PNR status will be checked immediately, and you will be able to view whether your ticket is confirmed (CNF), placed on the. (ii) On cancellation of confirmed reserved tickets between 48 hours and 12 hours before the train’s scheduled departure, cancellation charge will be 25% subject to minimum charge as per (i) aboveThus, the conditional probability that a random person is infected that has a positive test result is 0. Even though the composites showed lower. Capital Structure Assumptions. We just need to calculate the likelihood in the new time period of observation and multiply it. Normal distribution. For instance, it showed a 95 per cent probability of confirmation for the train ticket when general waiting list was three. ) if the o(1) term is O(VZ-~) for any constant a. Unit 5 Exploring bivariate numerical data. . Then, Bayes rule can be expressed as: P (A|B) =. 8413 – 0. Enter a problem Cooking Calculators. Then we will subtract the smaller value from the larger value: 0. g. n (S) = Total number of event. Below are some notations we use to show seat prediction in mouse-over bubble and PNR. Proof. Build a truth table for the formulas entered. CNF Refresh. Check. • This form is called a Conjunctive Normal Form, or CNF. cnf: # The MariaDB/MySQL tools read configuration files in the following order: # 0. Coefficient of variation (CV) calculator - to find the ratio of standard deviation ((σ) to mean (μ). Take advantage of this free Cumulative Probability Calculator tool to compute the chances of occurring two or more events. For math, science, nutrition, history. Upper bound on r k For any random clause with k literals, x1 + x2 +. You can use this Probability Calculator to determine the probability of single and multiple events. logical diagrams (alpha graphs, Begriffsschrift), Polish notation, truth tables, normal forms (CNF, DNF), Quine-McCluskey and other optimizations. First ,break the odds into 2 separate events: the odds of drawing a white marble (11) and the odds of drawing a marble of a different color (9). 2) and for bundles of fibrils (Fig. We are interested in the maximal blow-up of size when switching from the CNF repre- sentation to the DNF representation (or vice versa). Then, select the community cards, which are the cards dealt to the table and are available to all players. Where, n is the total number in the dataset. 3 Implementing the Logic Calculator In this section we describe the modules and functionality of the Logic. We always get confused while learning about the terms PCNF (Principal conjunction normal form) and CNF (Conjunction normal form), but there is a difference between both these terms. 96, then X is the 97. You. Find Normal Forms of Boolean Expression: Conjunctive normal form (CNF), including perfect. The construction goes as follows: For each variable in C, there is a corresponding variable in F . The CNF formula that represents this set of constraints is: (c1 ∨c6 ∨c7 ∨c8) ∧c2 ∧ (c3 ∨c5) ∧c4 ∧c9. It is showing RAC 32 and cnf probability of 86%. Cellulose nanofiber (CNF) nanopapers from garlic skin prepared by vacuum filtration were soaked in various concentrations of polyimide (PI) solution (0–15% w/v). Then, you can calculate FPR and FNR as below: from sklearn. The cumulative probability distribution is given below. en. 2. Area (probability) = 0. To use the poker hand odds calculator, follow these easy steps: First, select which two cards you've been dealt. KDA Calculator. For example, say we rolled 2 dice and we wanted to obtain a sum of 4. Each clause contains one or more literals (boolean variables). This Z-test calculator is a tool that helps you perform a one-sample Z-test on the population's mean. The Binomial Distribution Calculator Provide a table for: n = 5, p = 0. 1. Probability Theory. Step 1 − Eliminate epsilon productions. Recall that CNFs are conjuctions of disjunctions. with probability 1 – For m/n > c*, as n , problem is unsatisfiable with probability 1 • Conjecture proved true for k=2 and c*=1 • For k=3, current status is that c* is in the range 3. i– Backwards = i —t–. P - transition matrix, contains the probabilities to move from state i to state j in one step (p i,j) for every combination i, j. 2%, the probability of. logic. This type of tickets will be given a separate priority and confirmations will depend on the cancellations of a destination. For example, the probability of getting two or fewer successes when flipping a coin four times (p = 0. Proof: We reduce #SAT to this problem. This page will calculate exact binomial probabilities for situations of the general "k out of N" type, through various applications of the formula. 38125 for 10-sided dice; P2 = 0. the number of logical connectives in ’. You can also find an event's probability when you repeat the trial multiple times. Step 4: Write the Product of sums. P (¬A) + P (A) = 1. Then, proceed with entering journey details such as date, class of travel, destination. Simple to use Truth Table Generator for any given logical formula. Each clause contains one or more literals (boolean variables). n (E) = Represent the favorable outcome. The CNF consists of conjunctions of one or more clauses. Yeah, it is kind of obvious. For example, the calculator reports that the probability of getting AT MOST 4 school closings in the coming year is 0. Related Symbolab blog posts. 2. 13 $$ P(0) = 0. How to type. Therefore, we plug those numbers into the Binomial Calculator and hit the Calculate button. By reading the axis you can estimate the probability of a particular observation within that range: take the difference between 90. How does CNF probability work? People who do not have confirmed tickets can check for the probability of confirmation by clicking on ‘CNF Probability’ and it will be displayed in terms of per centage. Normal distribution formulas: probability density, cumulative distribution function and quantile function. With those two assumptions stated, we can calculate that the equity value of all three companies is $10 billion. – ∨¬ ∧ ¬ ∧ ∨ is a CNF –(∨¬∨) is a CNF. The Probability calculator allows you to calculate the probability of an event occurring by entering the number of events and the total number of outcomes. The following formula is in a matrix form, S 0 is a vector, and P is a matrix. 2a–c), right-handed chirality is observed both on the single fibril level (Fig. Descriptive Statistics Calculator - Find Arithmetic mean, mode, median, minimum, maximum of a data set. g. Which is now in CNF. probability-calculator. Enter the 10-digit PNR number found on the top left corner of a train ticket and go to the "PNR Status" button. For instance, it showed a 95 per cent probability of confirmation for the train ticket when general waiting list was three. For instance, it showed a 95 per cent probability of confirmation for the train ticket when general waiting list was three. Set theory studies the properties of sets, such as cardinality (the number of elements in a set) and operations that can be performed on sets, such as union, intersection, and complement. Conjunctive normal form (CNF) is an approach to Boolean logic that expresses formulas as conjunctions of clauses with an AND or OR. Hit the calculate button for results. In the picture, the index 1 is used for the state labeled C and the index 2 is used for the state labeled H. sergiouniversity. 15% CNF, the flexural toughness of 0. Free Statistics Calculator - find the mean, median, standard deviation, variance and ranges of a data set step-by-step We've updated our. – ∨ ¬∧ is not a CNF • An AND (∧) of CNF formulas is a CNF formula. hmmmm hmmmm. Statistics Calculator . In most cases, the ticket would get confirmed. 9 years ago. Standard normal distribution calculator (z table calculator) which also supports custom mean and sd (standard deviation, sigma). For example, if X = 1. 71293E−5 $$ Pie Chart for Probability Relative: The binomial probability calculator displays a pie chart for. ) Put in how many flips you made, how many heads came up, the probability of heads coming up, and the type of probability. It can calculate the probability of success if the outcome is a binomial random variable, for example if flipping. The positive square root of the variance is called the. 4. Sample space: The collection of all possible events is called sample space. r. 265 is the area on the left from the point P(λ = 5; x ≤ 4) = 0. Follow edited Sep 17, 2014 at 10:36. A phone, laptop or any other device with a web browser. It is 86%, as you mention in the post yourself. CNF Converter. Suppose X and Y are two independent random variables, each with the standard normal density (see Example 5. Calculating it involves analyzing. Unit 7 Probability. 0. Summing them up (you can use our fractions. high probability in HMM, low probability in PCFG • Probabilistic Regular Grammar Ni −→wjNk Ni −→wj Slide based on “Foundations of Statistical Natural Language Processing”by Christopher Manning and HinrichSchütze ∀n P w 1n P(w 1n)=1 P w∈L P(w)=1 Passenger 1: Confirmed: CNF:B3:26 (Booking Status: RLWL:6:GN) Total Fare: 860 Chart Prepared refreshed by: 1108853/Brandon12663^~ Full PNR Status History (10 statuses) Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. 2-SAT. Improve this answer. Converting to CNF. $egingroup$ I'm don't know any software, however, this problem feels like it should be quite trivial. Half 3-CNF Satisfiability: CLRS 34. By definition - for example Herbert B. Chi-square test calculation details Chi-square tests compare the observed (O) and expected (E) frequencies of the subjects. Our calculator construct a truth table for 4 variables of the given expression. 5-8 In the Half 3-CNF Satisfiability problem, we are given a 3-CNF (3 conjunctive normal form) formula φ with n variables and m clauses where m is even. Wolfram|Alpha works with Boolean algebra by computing truth tables, finding normal forms, constructing logic circuits and more. In fact, for either values of and , the 3-CNF is satisfiable. At this point, the statement is in Negation Normal Form (NNF) Then, to get the statement into CNF, distribute $lor$ over $land$for any probability distribution D for any † (where0 • † < 1 2) for any – (where0 • – < 1 algorithm L on input † and – and a set of random examples picked from any probability distribution D outputs at least with a probability 1¡–, concept h such that error(h;f) • †. P—wWe would like to show you a description here but the site won’t allow us. Statistics is about analyzing data, for instance the mean is commonly used to measure the “central tendency” of. Internet connection. Truth table calculator, CNF, DNF and Zhegalkin polynomial The online calculator allows you to quickly build a truth table for an arbitrary Boolean function or its vector, calculate perfect disjunctive and perfect conjunctive normal forms, find function representation in the form of the Zhegalkin polynomial, build a K-Map (Karnaugh Map), and. 5 percentile point of the standard normal distribution. Sorted by: 4. 1 Answer. Cellulose nanofibril (CNF) gel (11. If A and B are independent events, then the probability of A and B occurring together is given by. The team would win 5 out of 6 games and lose 1 of them. P (B), P (A|B), P (B|A) This calculator uses Bayes Rule (aka, Bayes theorem, the multiplication rule of probability) to compute the probability of one event, based on known probabilities of other events. Note, that the above-described situation may represent the early stages of the COVID. Use it to calculate: (a) P(X = 2). In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. Once you've done that, refresh this page to start using Wolfram|Alpha. The value of Willy’s factory is $500,000 if there is no flood and $0 if there is a flood. Applies commutative law, distributive law, dominant (null, annulment) law, identity law, negation law, double negation (involution) law, idempotent law, complement law, absorption law, redundancy law, de. Here is the definition of k -CNF formula: A conjunctive normal form (CNF) formula is a conjunction of disjunctions. Simply click Done to confirm the adjustments. In this section we show that the satis ability problem for 2-CNF formulas can be solved in polynomial time. If φ is a variable, then: return φ. 999%. What is CNF probability?The normal probability calculator functions as a standard normal probability calculator by offering probabilities for various confidence levels.