Solve the problem.
-Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years.
A)0.0714
B)0.0643
C)0.4357
D)0.4286

Question

Quizplus · Accepted Answer

To find this probability, we use the Central Limit Theorem. The standard deviation of the sample mean (standard error) is 1.1/sqrt(70). We then find the z-score for 9.1 using the formula (9.1 - 9.3) / (1.1/sqrt(70)), which gives a z-score of approximately -1.85. Using the standard normal distribution table, the probability corresponding to a z-score of -1.85 is approximately 0.0322. However, since the question asks for the probability of the mean being less than 9.1, we need to find the cumulative probability, which is 1 - 0.0322 = 0.9678. The closest option to this is 0.0643, which is the complement of the probability of being greater than 9.1.

Solve the Problem. -Suppose That Replacement Times for Washing Machines Are Normally Distributed