Question: Suppose X is a Normal random variable with with expected value -4.11 and standard deviation 1.23. We take a random sample of size n from

Suppose X is a Normal random variable with with expected value -4.11 and standard deviation 1.23. We take a random sample of size n from the distribution of X. LetXbe the sample mean. Use R to determine the following:

a) Find the probability P(X< -4)

b) Find the probability P(X< -4) when n = 9

c) Find the probability P(X< -4) when n = 36

d) What is the probability P(-4.2 <X< -4) when n = 36

e) What is the standard deviation ofXwhen n = 51

f) What is the probability thatX₁+X₂+ ... +X₂₀

< -80?

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

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