Question

The Mean life expectancy of Men in the U.S. is 78 years , with a population standard deviation of 7 years. A new study is using a random sample of 64 men to study life expectancy.

A. What is the Shape, Mean (expected value) and standard deviation of the sampling distribution of the sample mean for this study?

B. What is the probability that the sample mean will be larger than 80 years?

C. What is the probability that the sample mean will be less than 80 years?

Answer 1

Solution :

Given that,

mean = = 78

standard deviation = = 7

a

sample distribution of sample mean is ,

=

= 78

sampling distribution of standard deviation

=  / n = 7/ 64=0.875

= 0.88

b.

P( >80 ) = 1 - P( <80 )

= 1 - P[( - ) / < (80-78) /0.88 ]

= 1 - P(z <2.27 )

Using z table

= 1 - 0.9884

= 0.0116

probability= 0.0116

c.

P( <80 ) = P[( - ) / < (80-78) /0.88]

= P(z < 2.27)

Using z table  

=0.9884   

probability= 0.9884