gets an A is .4. (1) What is the probability that seven or fewer students receive A’s?(2) What is the probability that more than seven students receive A’s?(3) What is the probability that between 5 and 9 students (inclusive) will receive A’s?Solutionk=20 5Edward Fox and John Semple, 2020
MAST 6478 Data AnalyticsFor part (3), we will use Excel’s function BINOM.DIST.RANGE(n,p,klower,kupper). This function computes the probability of between klowerand kuppersuccesses in ntrials, includingklowerand kupper. Be careful to enter klowerand kupperin the function so that it reflects the range of successes that you are interested in.The Normal Distribution The mean and the variance (or alternatively the standard deviation) completely describe a normal distributionNorm.dist.range is NOT an excel function used for normal distribution calculationsThe sum of normal distributions has a normal distributionWhen a random variable Xcan take on any value in an interval, we call it a continuous random variableand describe the outcomes (which are too numerous to count) using a probability density function or PDF. Instead of talking about the probability that Xtakes on a specific value as we do with discrete distributions, with continuous distributions we talk about the probability that Xfalls within an interval such as [0, 10] or, more generally, [c, d]. We write the general probabilityPr(c≤X≤d). The probability that Xfalls in the interval [c, d] is the area under the PDF curve that is bounded on the left by c, on the right by d, and below by the x-axis. For continuous distributions, probability corresponds to the area under the curve.
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Normal Distribution, Probability distribution, Probability theory, Cumulative distribution function, John Semple, Edward Fox