Question

Suppose a simple random sample of size

nequals=36

is obtained from a population with

μ=81

and

sigma equals 6.

​(a) Describe the sampling distribution of

x overbarx.

​(b) What is

Upper P left parenthesis x overbar greater than 82.55 right parenthesisP x>82.55​?

​(c) What is

Upper P left parenthesis x overbar less than or equals 78.85 right parenthesisP x≤78.85​?

​(d) What is

Upper P left parenthesis 79.9 less than x overbar less than 82.85 right parenthesisP 79.9<x<82.85​?

Answer 1

Solution :

Given that,

mean = = 81

standard deviation = = 6

a) n = 36

=   = 81

= / n = 6 / 36 = 1

b) P( > 82.55) = 1 - P( < 82.55)

= 1 - P[( - ) / < (82.55 - 81) / 1 ]

= 1 - P(z < 1.55)

Using z table,    

= 1 - 0.9394

= 0.0606

c) P( 78.85 ) = P(( - ) / (78.85 - 81) / 1)

= P(z -2.15)

Using z table

= 0.0158

d) P(79.9 < < 82.85)  

= P[(79.9 - 81) /1 < ( - ) / < (82.85 - 81) / 1)]

= P(-1.10 < Z < 1.85)

= P(Z < 1.85) - P(Z < -1.10)

Using z table,  

= 0.9678 - 0.1357   

= 0.8321