Answered: surements are in inches. Using R and…

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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Question

Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.
a) What is the probability that X < 59?

b) What is the probability that X > 59?

c) What is the probability that all of the 180 measurements are greater than 59?

d) What is the expected value of S?

e) What is the standard deviation of S?

f) What is the probability that S-180*65 >10?

g) What is the standard deviation of S-180*65

h) What is the expected value of M?

i) What is the standard deviation of M?

j) What is the probability that M >65.41?

k) What is the standard deviation of 180*M?

l) If the probability of X > k is equal to .3, then what is k?