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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?
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Answer Attempt tout of 20
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(C) Watch Video $\newline$ Show Examples $\newline$ 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? $\newline$ Statistics Calculator $\newline$ Answer Attempt tout of $20$ $\newline$ Submit Answer

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Interpret confidence intervals for population means

Full solution

Q. (C) Watch Video

\newline

Show Examples

\newline

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?

\newline

Statistics Calculator

\newline

Answer Attempt tout of

20

\newline

Submit Answer

Calculate z-score: Calculate the z-score for Sophie's score of $129$ using the formula $z = \frac{X - \mu}{\sigma}$ , where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. $\newline$ $z = \frac{129 - 110}{10}$ $\newline$ $z = \frac{19}{10}$ $\newline$ $z = 1.9$
Lookup z-score probability: Look up the z-score of $1.9$ in the standard normal distribution table to find the probability of scoring less than $129$ . The table gives us the probability of scoring less than a z-score of $1.9$ , which is approximately $0.9713$ or $97.13\%$ .
Calculate percentage higher: Calculate the percentage of games where Sophie scores higher than $129$ by subtracting the probability of scoring less than $129$ from $1$ (or $100\%$ ). $\newline$ Percentage higher than $129 = 1 - 0.9713$ $\newline$ Percentage higher than $129 = 0.0287$
Convert decimal to percentage: Convert the decimal to a percentage and round to the nearest tenth. $\newline$ Percentage higher than $129 = 0.0287 \times 100$ $\newline$ Percentage higher than $129 = 2.87\%$ $\newline$ Rounded to the nearest tenth: $2.9\%$

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