> Question A normal distribution is observed from the number of points per game for a certain basketball player. If the mean is 15 points and the standard deviation is 3 points, what is the probability that in a randomly selected game, the player scored greater than 24 points?

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absor201 absor201 · Answer 1 · 2020-11-25T15:15:37+01:00

Answer:

The probability that in a randomly selected game, the player scored greater than 24 points is 0.0013 or 0.13%

Step-by-step explanation:

Given that

Mean = μ = 15 points

SD = σ = 3 points

For calculating probability for a data point, first of all we have to calculate the z-score of the value.

We have to find the probability of score greater than 24, then the z-score of 24 is:

z-score = (x-μ)/σ

z = (24-15)/3

z = 9/3

z = 3

Now we have to use the z-score table to find the probability of z<3 then it will be subtracted from 1 to find the probability of z>3

So,

[tex]P(z<3) = 0.9987\\P(z>3) = 1 - P(z<3) = 1-0.9987 = 0.0013[/tex]

Converting into percentage

0.0013 * 100 = 0.13%

Hence,

The probability that in a randomly selected game, the player scored greater than 24 points is 0.0013 or 0.13%