Question

In a random sample of 60 computers, the mean repair cost was

$150with a population standard deviation of $36. Construct a
99%confidence interval for the population mean.

Answer 1

Explanation:

We want to construct a 99% confidence interval for the population mean

Number of sample, n = 60

Mean, u = $150

Standard deviation, s = $36

For a confidence level of 99%, the corresponding z value is 2.58. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

150 ± 2.58 × 36/√60

= 150 ± 2.58 × 4.65

= 150 ± 11.997

The lower end of the confidence interval is 150 - 11.997 = 138.003

The upper end of the confidence interval is 150 + 11.997 =161.997

Therefore, with 99% confidence interval, the population mean is between $138.003 and $161.997