Question

In a random sample of 60 computers, the mean repair cost was $150 with a population standard deviation of $36. Use this sample data to construct a 90% confidence interval for the mean repair cost, μ, of all such computers.

A. $145 to $155
B. $140 to $160
C. $135 to $165
D. $130 to $170

Answer 1

The 90% confidence interval for the mean repair cost is approximately $145 to $155.

Step-by-step explanation:

To construct a 90% confidence interval for the mean repair cost, we can use the formula:

Lower limit: mean - (Z * (population standard deviation / sqrt(sample size)))

Upper limit: mean + (Z * (population standard deviation / sqrt(sample size)))

Plugging in the given values, we have:

Lower limit = 150 - (1.645 * (36 / sqrt(60)))

Upper limit = 150 + (1.645 * (36 / sqrt(60)))

Calculating these values, we get:

Lower limit ≈ 145.23

Upper limit ≈ 154.77

So, the 90% confidence interval for the mean repair cost is approximately $145 to $155.