Question

> 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? ​

Answer 1

To calculate the probability of scoring greater than 24 points, we determine the z-score of 3 by using the mean and standard deviation, then find the corresponding probability using a z-table or software, resulting in a 0.13% chance.

Step-by-step explanation:

To find the probability that a basketball player scored greater than 24 points in a game, we can use the properties of the normal distribution. Given a mean (μ) of 15 points and a standard deviation (σ) of 3 points, we calculate a z-score for 24 points.

The z-score is given by:

Z = (X - μ) / σ

Where X is the score of interest (24 points).

Z = (24 - 15) / 3

Z = 9 / 3

Z = 3

This z-score tells us how many standard deviations above the mean our score of interest is. To find the probability associated with this z-score, we utilize the z-table or a statistical software. Since z-tables typically provide the area to the left of a z-score, we need to subtract this value from 1 to get the area to the right (which represents scoring more than 24 points).

The area to the left of a z-score of 3 is approximately 0.9987. Therefore, the probability of scoring more than 24 points is:

P(X > 24) = 1 - P(Z < 3)

P(X > 24) = 1 - 0.9987

P(X > 24) = 0.0013

So there's a 0.13% chance that the player scores more than 24 points in a randomly selected game.

Answer 2

Answer:0.15%

Step-by-step explanation:

Notice that 24 points is three standard deviations greater than the mean. Based on the Empirical Rule, 99.7% of the player's game scores are within three standard deviations of the mean. Since the normal distribution is symmetric, this implies that 0.15% of the player's game scores are greater than three standard deviation more than the mean.