Question

After collecting the data, Maria finds that the number of points per game for a certain basketball player is normally distributed with mean 14 points and standard deviation 2 points. What is the probability that in a randomly selected game, the player scored more than 8 points? Enter your answer as a percent rounded to 2 decimal places if necessary. Include the percent symbol % in your answer.

Answer 1

Explanation:

Since the number of points per game for a certain basketball player is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = number of points per game

µ = mean

σ = standard deviation

From the information given,

µ = 14 points

σ = 2 points

The probability that in a randomly selected game, the player scored more than 8 points is expressed as

P(x > 8) = 1 - P(x ≤ 8

For x = 8,

z = (8 - 14)/2 = - 3

Looking at the normal distribution table, the probability corresponding to the z score is 0.00135

P(x > 8) = 1 - 0.00135 = 0.9987

Converting to percentage, it becomes

0.9987 × 100 = 99.87%