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?
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.