Question

Problem 4 Car mufflers are constructed by nearly automatic machines. One manufacturer finds that, for any type of car muffler, the time for a person to set up and complete a pro-duction run has a normal distribution with mean 1.82 hours and standard deviation 1.20. What is the probability that the sample mean of the next 40 runs will be from 1.65 to 2.04 hours?

Answer 1

Answer:

Standard error =sd/sqrt(n) = 1.20/sqrt(40) =0.1897

Z value for 1.65, z =(1.65-1.82)/0.1897 = -0.90

Z value for 2.04, z =(2.04-1.82)/0.1897 =1.16

P( 1.65< mean x<2.04) = P( -0.90<z<1.16)

=P( z < 1.16) – P( z < -0.90)

=0.8770 -0.1841

=0.6929