A city official in Seattle randomly sampled 21 local bicycle commuters in 2019 and asked them how long it takes them typically to bike from home to his or her destination.

This resulted in the following commute times, in minutes: 25 14 17 24 26 23 16 11 22 19 32 26 18 21 10 21 7 18 17 24 24

(a) Illustrate that this dataset is approximately normally distributed, by constructing a relative-frequency histogram using the interval [0, 5) as the first class, the interval [5, 10) as the second class, etc.

(b) Find a point estimate for , where denotes the average commute time for all bicycle commuters in Seattle.

(c) A point estimate for , the standard deviation of the commute times for all bicycle commuters in Seattle, is given by the sample standard deviation s which is 6.05 minutes for this dataset. Use this value to obtain a 95% confidence interval for .

(d) Interpret your result in part (c).

(e) If the confidence level in part (c) is changed to 90%, does the confidence interval get narrower or wider? Explain