One feature smartphone manufacturers use in advertising is the amount of time one can talk before recharging the battery. Below are 13 values from a random sample of the talk-time (in minutes) of smartphones running on lithium-ion batteries. The summary statistics are x̅ = 553, s = 227, Q1 = 420, median = 450, Q3 = 650. Talk time: 320, 360, 760, 580, 1050, 900, 360, 500, 420, 420, 650, 420, 450.
a. Construct an appropriate graph (dot plot, stem and leaf plot, histogram, box plot) to describe the shape of the distribution. What assumptions are needed to construct a 95% confidence interval for m, the mean talk time? Point out any assumptions that seem questionable.
b. Check whether this data set has any potential outliers according to the criterion of

 (i) 1.5 * IQR below Q1 or above Q3 

(ii) 3 standard deviations from the mean.
c. Using the summary statistics, show that the 95% confidence interval is (416, 690). Interpret it in context.
d. The value 1050 is quite a bit larger than the others. Delete this observation, find the new mean and standard deviation, and construct the 95% confidence interval for μ without this observation. How does it compare to the 95% confidence interval, using all the data?