When Sophie goes bowling, her scores are normally distributed with a mean of 110 and a standard deviation of 10. What percentage of the games that Sophie bowls does she score higher than 129, to the nearest tenth?

Answer 1

To find the percentage of games that Sophie scores higher than 129, we first need to calculate the z-score for a score of 129.

The z-score formula is:

z = (X - μ) / σ

Where:
X = 129 (the score we want to find the z-score for)
μ = 110 (mean)
σ = 10 (standard deviation)

z = (129 - 110) / 10
z = 19 / 10
z = 1.9

Next, we will use a z-score table or a calculator to find the percentage of games corresponding to a z-score of 1.9. From the z-score table, we find that the percentage of games scored higher than a z-score of 1.9 is approximately 3.3%.

Therefore, approximately 3.3% of the games that Sophie bowls, she scores higher than 129.