Question

At the Canada Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 99 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves.

a.54 mph to 144 mph

b. 39 mph to 159 mph

c. 144 mph to 189 mph

d. 69 mph to 129 mph

Answer 1

In this question, it is asked to find out the confidence interval so-

we have,

mean = mu = 99

st. deviation = 15

confidence level = 8/9 = 0.89 = 89% ~ 90%

critical value at 89% = 1.64

now the margin of error = 15 * 1.64 = 24.6 ~ 25

confidence interval = 99+- 25 = (74, 124)

so the closest interval that will contain the serve speed for at least eight-ninth times can be given as-

(69, 129)