Question

Julia enjoys jogging. She has been jogging over a period of several years, during which time her physical condition has remained constantly good. Usually she jogs 2 miles per day. During the past year Julia recorded how long it took her to run 2 miles. She has a random sample of 90 of these times. For these 90 times the mean was 15.60 minutes and the standard deviation s=1.80 minutes. Find the margin of error (round to 2 decimal places) and the 95% confidence interval for Julia’s average running time.

Answer 1

To find the margin of error and the 95% confidence interval for Julia's average running time, we can use the formula: Margin of Error = Z * (Standard Deviation / sqrt(n)). Given the sample mean, standard deviation, and sample size, we can calculate the margin of error and the confidence interval.

Step-by-step explanation:

To find the margin of error and the 95% confidence interval for Julia's average running time, we can use the formula:

Margin of Error = Z * (Standard Deviation / sqrt(n))

Confidence Interval = (Sample Mean - Margin of Error, Sample Mean + Margin of Error)

Given that the sample mean is 15.60 minutes, the standard deviation (s) is 1.80 minutes, and the sample size (n) is 90, we can calculate the margin of error:

Margin of Error = (1.96 * 1.80) / sqrt(90) = 0.35 minutes (rounded to 2 decimal places)

Therefore, the 95% confidence interval for Julia's average running time is (15.25 minutes, 15.95 minutes).