The number of passes completed by Ben Roethlisberger, quarterback for the Pittsburgh Steelers, was recorded for each of the 15 regular season games in which he played during the fall of 2017 (www.ESPN.com).

202244243330191714173318222324

(a)

A stem and leaf plot of then= 15 observations is shown below.

Stem and Leaf Display: RoethlisbergerStem-and-leaf of RoethlisbergerN = 15Leaf Unit = 1.0114517789(6)2022344424303313144

Based on this plot, is it reasonable to assume that the underlying population, Ben Roethlisberger's entire career, is approximately normal, as required for the one-samplet-test? Explain.

The shape of the stem and leaf plot is not perfectly normal, but since the sample size is so small, the normality assumption cannot be rejected.

The shape of the stem and leaf plot is not perfectly normal, and since the sample size is large enough that we should expect a perfectly normal sample distribution, the normality assumption can be rejected.

(b)

Calculate the mean and standard deviation for Ben Roethlisberger's per game pass completions. (Round your standard deviation to four decimal places.)

meanpass completions standard deviationpass completions

(c)

Construct a 95% confidence interval to estimate the average pass completions per game for Ben Roethlisberger. (Round your answers to three decimal places.)

pass completions topass completions