Question

A simple random sample of size

nequals=1212

is obtained from a population with

muμequals=6868

and

sigmaσequals=1616.

​(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 overbarx.

​(b) Assuming the normal model can be​ used, determine

​P(x overbarxless than<72.172.1​).

​(c) Assuming the normal model can be​ used, determine

​P(x overbarxgreater than or equals≥69.669.6​).

Answer 1

Solution :

Given that ,

a ) mean = = 68

standard deviation = = 16

n = 12

= 68

= / n = / = 16/ 12 = 4.6188

b ) P( < 72.1 )

= P[( - ) / < (72.1- 68) / 4.6188)

= P(z <0.89 )

p = 0.8133

c )

P( > 69.6 ) = 1 - P( < 69.6 )

= 1 - P[( - ) / < (69.6 - 68) /4.6188 )

= 1 - P(z < 0.35 )

= 1 - 0.6368

p= 0.3632