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Question 7) Suppose X is a Normal random variable with with expected value 31 and standard...

Question 7) Suppose X is a Normal random variable with with expected value 31 and standard deviation 3.11. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following:

a) Find the probability P(X>32.1):

b) Find the probability P(X >32.1) when n = 4:

c) Find the probability P(X >32.1) when n = 25:

d) What is the probability P(31.8 <X <32.5) when n = 25?

e) What is the standard deviation of X when n = 19?

f) What is the probability that X1 + X2 + ... +X20 > 630?

g) Copy your R script for the above into the text box here.

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