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.
(1 point)
Responses
0.4286
0.0714
0.0643
0.4357
To solve this problem, we need to use the Central Limit Theorem to find the probability.
First, we need to find the standard error of the sampling distribution of the sample mean, which is calculated as the standard deviation of the population (1.1 years) divided by the square root of the sample size (70).
Standard Error = 1.1 / sqrt(70) = 0.1317
Next, we need to calculate the z-score that corresponds to a sample mean of 9.1 years:
z = (9.1 - 9.3) / 0.1317 = -1.52
Now, we can find the probability that the sample mean of 70 randomly selected washing machines is less than 9.1 years by looking up the z-score in the standard normal distribution table.
Using the standard normal distribution table, we find that the probability corresponding to a z-score of -1.52 is approximately 0.0643.
Therefore, the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years is approximately 0.0643.
Therefore, the correct response is:
0.0643