Question

A simple random sample of size nequals37 is obtained from a population with muequals61 and sigmaequals14. ?(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample? mean? Assuming that this condition is? true, describe the sampling distribution of x overbar. ?(b) Assuming the normal model can be? used, determine ?P(x overbarless than65.1?). ?(c) Assuming the normal model can be? used, determine ?P(x overbargreater than or equals62.4?).

Answer 1

Solution:

Given that,

= 61

= 14

n = 37

So,

a ) = 61

=  ( / ) = (14 /37  ) = 2.3016

p (   < 65.1)

= p ( - /) < (65.1 - 61/ 2.3016 )

= p ( z < 4.1/ 2.3016 )

= p ( z < 1.78)

Using z table

= 0.9625

Probability = 0.9625

c ) ( 62.4 )

= 1 - p (    62.4 )

= 1 - p ( - /)   (62.4 - 61 /2.3016)

= 1 - p( z   1.4 / 2.3016 )

= 1 - p ( z 0.61 )   

Using z table

= 1 - 0.7291

= 0.2709

Probability = 0.2709