Question

A simple random sample of size

nequals=8181

is obtained from a population with

mu equals 73μ=73

and

sigma equals 18σ=18.

​(a) Describe the sampling distribution of

x overbarx.

​(b) What is

Upper P left parenthesis x overbar greater than 75.9 right parenthesisP x>75.9​?

​(c) What is

Upper P left parenthesis x overbar less than or equals 68.8 right parenthesisP x≤68.8​?

​(d) What is

Upper P left parenthesis 71 less than x overbar less than 77.8 right parenthesisP 71<x<77.8​?

Answer 1

Solution :

Given that ,

mean = = 73

standard deviation = = 18

n = 81

a) =   = 73

= / n = 18 / 81 = 2

b) P( > 75.9 ) = 1 - P( < 75.9 )

= 1 - P[( - ) / < ( 75.9 - 73 ) / 2 ]

= 1 - P(z < 1.45 )

Using z table

= 1 - 0.9265

= 0.0735

c) P( 68.8 )

= P(( - ) / ( 68.8 - 73) / 2 )

= P(z -2.1 )

Using z table

=0.0179

d) P( 71 < < 77.8 )

= P[( 71 - 73 ) / 2 < ( - ) / < ( 77.8 - 73 ) / 2 )]

= P( -1.00 < Z < 2.4 )

= P(Z < 2.4 ) - P(Z < -1.00 )

Using z table

= 0.9918 - 0.1587

= 0.8331