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6. Let the random variable Z follow a standard normal distribution. In each case, obtain a numerical answer and express this answer in terms of an integral of the standard normal density function (for which we can use the symbol p(x)). a) Find P(Z < 1.20). b) Find P(Z > 1.33). c) Find P(Z < -1.70).

6. Let the random variable Z follow a standard normal distribution. In each case, obtain a numerical answer and express this answer in terms of an integral of the standard normal density function (for which we can use the symbol p(x)). a) Find P(Z < 1.20). b) Find P(Z > 1.33). c) Find P(Z < -1.70).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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6. Let the random variable Z follow a standard normal distribution. In each case, obtain a numerical answer and express this answer in terms of an integral of the standard normal density function (for which we can use the symbol o(x)). a) Find P(Z < 1.20). b) Find P(Z > 1.33). c) Find P(Z < -1.70). d) Find P(Z > -1.00). e) Find P(1.20 < Z < 1.33). f) Find P(-1.70 < Z < 1.20). g) Find P(-1.70 < Z < −1.00). 7. Scores on an achievement test are known to be normally distributed, with mean 420 and standard deviation 80. (a) For a randomly chosen person taking this test, what is the probability of a score between 400 and 480? (b) What is the minimum score needed in order to be in the top 10% of all people taking the test? (c) For a randomly chosen individual, state, without doing the calculations, in which of the following ranges his or her score is most likely to be: 400-440, 440-480, 480-520 or 520-560? (d) In which of the ranges listed in c) is the individual's score least likely to be? (e) Two people taking the test are chosen at random. What is the probability that at least one of them scores more than 500 points? 8. We obtained in class estimates of the density of the St. Louis Fed's financial stress index. It would not, however, make sense to obtain the density of US GDP. Why not?
Transcribed Image Text:6. Let the random variable Z follow a standard normal distribution. In each case, obtain a numerical answer and express this answer in terms of an integral of the standard normal density function (for which we can use the symbol o(x)). a) Find P(Z < 1.20). b) Find P(Z > 1.33). c) Find P(Z < -1.70). d) Find P(Z > -1.00). e) Find P(1.20 < Z < 1.33). f) Find P(-1.70 < Z < 1.20). g) Find P(-1.70 < Z < −1.00). 7. Scores on an achievement test are known to be normally distributed, with mean 420 and standard deviation 80. (a) For a randomly chosen person taking this test, what is the probability of a score between 400 and 480? (b) What is the minimum score needed in order to be in the top 10% of all people taking the test? (c) For a randomly chosen individual, state, without doing the calculations, in which of the following ranges his or her score is most likely to be: 400-440, 440-480, 480-520 or 520-560? (d) In which of the ranges listed in c) is the individual's score least likely to be? (e) Two people taking the test are chosen at random. What is the probability that at least one of them scores more than 500 points? 8. We obtained in class estimates of the density of the St. Louis Fed's financial stress index. It would not, however, make sense to obtain the density of US GDP. Why not?
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