Question

The average estimate for the body repair on an automobile is $1540. From insurance records it has been determined that the population standard deviation is $640.

A. What is the probability of selecting a sample of 49 and the sample mean being above $1600?

Answer 1

Amount of people does not affect the result.

$$P(x>1600)=P(x-1540>60)=P\left(\frac{x-1540}{640}\right)^{\frac{3}{2}}$$

=1-F(3/32), where F(3/32)- is from the table of stand. Normal distribution.

$$1-F(3/32)=1-0.5359=0.4641$$