Question

A simple random sample of size nequals47 is obtained from a population with muequals67 and sigmaequals16. ?(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 than70.9?). ?(c) Assuming the normal model can be? used, determine ?P(x overbargreater than or equals68.9?).

Answer 1

Solution:

Given that,

= 67

= 16

n = 47

So,

a ) = 67

=  ( / ) = (16 /47  ) = 2.3334

b ) p (   < 70.9)

= p ( - /) < (70.9 - 67/ 2.3334 )

= p ( z < 3.9 / 2.3334 )

= p ( z < 1.67)

Using z table

= 0.9525

Probability = 0.9525

c ) ( 68.9 )

= 1 - p (    68.9 )

= 1 - p ( - /)   (68.9 - 67 /2.3334 )

= 1 - p( z   1.9 / 2.3334 )

= 1 - p ( z 0.81 )   

Using z table

= 1 - 0.7910

= 0.2090

Probability = 0.2090