Question

# Suppose X is a Normal random variable with with expected value 31 and standard deviation 3.11....

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

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

x.mean=31
x.sd=3.11
n=19
xbar.sd=(x.sd)/sqrt(n)
xbar.sd

-------------------------------------------------------------------------

(b)

x.mean=31
x.sd=3.11
n=20
xsum.mean=n*(x.mean)
xsum.sd=sqrt(n)*(x.sd)
ans=1-pnorm(630,mean=xsum.mean,sd=xsum.sd)
ans

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