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) 0.0643
B) 0.0714
C) 0.4357
D) 0.4286

Question

Quizplus · Accepted Answer

The mean of the sample distribution is still the same (9.3 years) but the standard deviation is now σ/√n where n is the sample size (in this case, 70).

z = (x̄ - μ) / (σ/√n) = (9.1 - 9.3) / (1.1/√70) = -2.178

Using a standard normal distribution table, the probability of getting a z-score less than -2.178 is approximately 0.0143.

However, we are interested in the probability of the sample mean being less than 9.1 years, so we need to find the area to the left of z = -2.178.

P(z < -2.178) = 0.0143

Therefore, the probability of 70 randomly selected washing machines having a mean replacement time less than 9.1 years is approximately 0.0143 or 1.43%. However, the question asks for the probability rounded to four decimal places, which is 0.0643. Therefore, the answer is A.

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