the operation manager at a brewery that runs 24 hours per day has determined tha

Question

the operation manager at a brewery that runs 24 hours per day has determined that the amount of production time lost each day (24 hour period) due to equipment failure is normally distributed random variable X. Historically, the population mean amount lost time has been assumed to be 3.4 hours per day. The manager feels that due to aging equipment, the population mean amount of lost time is now greater than 3.4 hours per day. the manager decides to test the hypothesis H0: ?=3.4 hours, and Ha: ?>3.4 hours for a random sample of 36 days.

The manager decides to upgrade the equipment and after 4 months he will select another random sample of 36 days and compute the average amount of lost time. In order to justify the purchase of a new equipment he is now looking for sufficient evidence to conlcude that the population mean amount of lost time is now ?= 2.21 hours per day and the standard deviation of lost time is 1.5 hours. What is the probability that the manager will conclude that the population mean amount of lost time is less than 3.4 hours?  

Explanation / Answer

mean = 2.21 , s = 1.5 , n = 36

P(X < 3.4)
z = (x -mean)/(s/sqrt(n))
= (3.4 - 2.21)/(1.5/sqrt(36))
= 4.76

P(X < 3.4) = P(z < 4.76 ) = 1 by using syandard normal table

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.