Answered: The Normal Distribution. The function…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Normal Distribution. The function NORMDIST(x, mu, sigma, TRUE) computes the probability that a normal observation with a fixed mean (mu) and standard deviation (sigma) is less than x. There is also a function for computing the inverse operation: the function NORMINV(p, mu, sigma) computes a value x such that the probability that a normal observation is less than x is equal to P. A. Compute the probability that an observation from a N(3, 5) population is less than 7. B. Find the number x such that P{ N(4, 4) < x } = .75, i.e., such that a normal observation with mean 4 and standard deviation 4 has probability .75 of being less than x. C. If the heights of 17-year-old girls are known to be normally distributed with mean 64 inches and standard deviation 3 inches, how tall must Taylor be when she is 17 so that she will be taller than 73% of other girls her age?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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