Question

In a random sample of 26 laptop computers, the mean repair cost was $149 with a standard deviation of $35. Assume the population has a normal distribution. Answer parts (a) and (b) 12(a). Calculate a 95% confidence interval for the population mean, μ.

a) $122.63 to $175.37
b) $135.55 to $162.45
c) $140.21 to $157.79
d) $112.43 to $185.57

Answer 1

To calculate a 95% confidence interval for the population mean, we will use the sample mean and standard deviation along with the critical value. The margin of error is calculated by multiplying the standard deviation by the critical value. The confidence interval is the sample mean plus or minus the margin of error.

Step-by-step explanation:

To calculate a 95% confidence interval for the population mean, we will use the formula:

Confidence Interval = sample mean ± margin of error

Using the given information, the sample mean is $149 and the standard deviation is $35. The margin of error can be calculated by multiplying the standard deviation by the critical value.

For a 95% confidence interval, the critical value is 1.96.

So, the margin of error = 1.96 * ($35 / sqrt(26)) ≈ $12.99

Therefore, the 95% confidence interval for the population mean is $149 ± $12.99, which is approximately $136.01 to $161.99.