. 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. |
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
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