Question

Construct a 95% confidence interval for the population mean, p Assume the population has a normal distribution. In a random sample of 26 computers, the mean repair cost was $146 with a standard deviation of $31.

Answer 1

For this problem with a sample mean of $146, standard deviation of $31, and sample size of 26, the 95% confidence interval is approximately ($133.04, $158.96).

Step-by-step explanation:

To construct a 95% confidence interval for the population mean, we can use the formula: (sample mean - margin of error, sample mean + margin of error).

The margin of error is calculated as:

(critical value * standard deviation) / sqrt(sample size).

For this problem, the sample mean is $146, the standard deviation is $31, the sample size is 26, and the critical value for a 95% confidence level is 1.96.

Plugging in these values, we get:

(146 - (1.96 * 31 / sqrt(26)), 146 + (1.96 * 31 / sqrt(26))).

Evaluating this, we find that the 95% confidence interval for the population mean is approximately ($133.04, $158.96).