Question

. An automotive repair shop has determined that the average service time on an automobile is 2 hours with a standard deviation of 32 minutes. A random sample of 64 services is selected.

a.	What is the probability that the sample of 64 will have a mean service time greater than 114 minutes?
b.	Assume the population consists of 400 services. Determine the standard error of the mean.

                                                                                                                                                                                 

Answer 1

Solution :

(a)

= / n = 32 / 64 = 4

P( > 114) = 1 - P( < 114)

= 1 - P[( - ) / < (114 - 120) / 4]

= 1 - P(z < -1.5)

= 0.9332

(b)

Standard error = / n = 32 / 400 = 1.6