Question

Jamie's points per game of bowling are normally distributed with a standard deviation of 14 points. If Jamie scores 92 points, and the z-score of this value is −4, then what is her mean points in a game?

Answer 1

Answer: To find the mean points in a game for Jamie, we can use the formula for z-score:

z = (X - μ) / σ

where:

z = z-score

X = observed value (score of 92 points in this case)

μ = mean points in a game (what we need to find)

σ = standard deviation (given as 14 points)

Given that the z-score of 92 points is -4, we can write the equation as:

-4 = (92 - μ) / 14

Now, solve for μ (mean points in a game):

-4 * 14 = 92 - μ

-56 = 92 - μ

Now, isolate μ on one side:

μ = 92 - 56

μ = 36

So, Jamie's mean points in a game is 36.