Question

Assume that the average number of of points scored in a typical high school basketball game is 60 (total for both theams_ The standard deviation is 20 points. What percentage of games have a total between 55 and 75 points? (Draw histogram to help.)

Answer 1

SOLUTION:

From given data,

Assume that the average number of of points scored in a typical high school basketball game is 60 (total for both theams_ The standard deviation is 20 points. What percentage of games have a total between 55 and 75 points? (Draw histogram to help.)

We have,

Mean = $\mu$ = 60

Standard deviation = $\sigma$ = 20

Z = (X - $\mu$) / $\sigma$ = (X - 60) / 20

We have to find the percentage of games have a total between 55 and 75 points.

P(55 < X < 75)

At X = 55 the value of Z is

Z =  (55 - 60) / 20

Z = -5 / 20

Z = -0.25

At X = 75 the value of Z is

Z =  (75 - 60) / 20

Z = 5 / 20

Z = 0.25

P(55 < X < 75) = P((55 - 60) / 20 < Z < (75 - 60) / 20)

P(55 < X < 75) = P( -0.25 < Z < 0.25)

P(55 < X < 75) = P(Z < 0.25) - P(Z < - 0.25)

P(55 < X < 75) = 0.59871 - 0.40129

P(55 < X < 75) = 0.1974

Now the percentage of games have a total between 55 and 75 points.

P(55 < X < 75) = 19.74 %

Diagram of Histogram 19.74% area Z 1 660 a Sto. Tot 7 Scanned with CamScanner

Please thumbs-up / vote up this answer if it was helpful. In case of any problem, please comment below. I will surely help. Down-votes are permanent and not notified to us, so we can't help in that case.