Question

Suppose a simple random sample of size

nequals=8181

is obtained from a population that is skewed right with

mu equals 78μ=78

and

sigma equals 9σ=9.

​(a) Describe the sampling distribution of

x overbarx.

​(b) What is

Upper P left parenthesis x overbar greater than 79.15 right parenthesisP x>79.15​?

​(c) What is

Upper P left parenthesis x overbar less than or equals 75.5 right parenthesisP x≤75.5​?

​(d) What is

Upper P left parenthesis 76.95 less than x overbar less than 80 right parenthesisP 76.95<x<80​?

​(a) Choose the correct description of the shape of the sampling distribution of

x overbarx.

A.

The distribution is approximately normal.

B.

The distribution is skewed right.

C.

The distribution is skewed left.

D.

The distribution is uniform.

E.

The shape of the distribution is unknown.

Answer 1

The R-CODE is

#b)
1-round(pnorm(1.15),4)
[1] 0.1251
#c)
round(pnorm(-2.5),4)
[1] 0.0062
#d)
round(pnorm(2),4)-round(pnorm(-1.05),4)
[1] 0.8303