Question

Hundreds of cross-country skiers participate in a race during Winter Carnival weekend. A student is interested in μ, the population mean number of minutes needed to complete the race among all the skiers. Assume the population is normally distributed. The standard deviation is known to be σ = 17.7 minutes. If the sample mean among a random sample of 16 skiers is 51.8 minutes, what is the 95% confidence interval for μ?

Answer 1

Given that, sample size (n) = 16, sample mean = 51.8 minutes

and population standard deviation ( σ ) = 17.7 minutes

A 95% confidence level has significance level of 0.05 and critical value is,

The 95% confidence interval for the population mean (μ) is,

Therefore, required confidence interval is, (43.127, 60.473).