Question 3 involves statistics

Question

Isabella's points per game of bowling are normally distributed with a standard deviation of 8 points. If Isabella scores 148 points, and the z-score of this value is 3, then what is her mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 150 points, you would enter 150.

Answer 1

For this question, we need to use the z-score formula to work backwards and solve for the mean.

The z-score formula is:

z = (X - mean) / standard deviation

In this case, we know that z = 3, X = 148, and standard deviation = 8, so we just plug those values in.

3 = (148 - mean) / 8

Start by multiplying both sides by 8 to cancel out the denominator. That gives you:

24 = 148 - mean

Subtract 148 from both sides to get:

-124 = -mean

So, the mean is 124.