At the U. S. 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 100 miles per hour (mph) and the standard deviation of the serve speeds was 10 mph.
Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds?
Speeds: 65 mph, 110 mph, and 120 mph.

The speed of 65 mph is an outlier in the distribution of the player's serve speeds

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100 mph

Standard Deviation, σ = 10 mph

Formula:

Outlier on basis of z-score:

Calculation of z-score:

Thus, the speed of 65 mph is an outlier in the distribution of the player's serve speeds as the corresponding z-score is less than -3.

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb