surements are in inches. Using R and write the code out. a) What is the probability that X < 59?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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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?

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