A researcher wants to estimate the average time a person spends commuting to Boston. The researcher chooses a random sample of 22 people and finds that their average commute is 49 minutes with a standard deviation of 23 minutes. Assume that commute times are normally distributed.

(a) Why are we allowed to assume that thesampling distributionin this problem is approximately normal?

The population standard deviation is known.

The population is normally distributed.

The margin of error is unknown.

The sample size is large enough.

(b) Which distribution should be used to find the critical value?

The z-distribution because the sample mean is large enough.

The z-distribution becauseis known.

The t-distribution because the sample size is small.

The t-distribution becauseis unknown.

(c) Construct a 90% confidence interval for the true average commute time.

lower limit

upper limit

margin of error