Question

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 X_{1} + X_{2} +
... +X_{20} > 630?

**PLEASE ANSWER IN R SCRIPT**

Answer #1

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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