Assume that all variable are approximately normally distributed.

Distance Traveled to Work A recent Study of 28 employees of XYZ company showed that the mean of the distance they traveled to work was 14.3 miles. The standard deviation of the sample mean was 2 miles. Find the 95% confidence interval of the true mean. If a manager wanted to be sure that most of his employees would not be late, how much time would he suggest they allow for the commute if the average speed were 30 miles per hour?

Answer

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(a)

The mean distance traveled by 28 employees of XYZ company was 14.3 miles.

The standard deviation of the sample mean was 2 miles.

We are asked to find the 95% CI of the true mean.

How much time would manager suggest they allow for the commute if the average speed were 30 miles per hour?

We have given

Formula for a Specific Confidence Interval for the Mean When Is Unknown

The degrees of freedom are

We can calculate the value of as,