Question

When Nayeli goes bowling, her scores are normally
distributed with a mean of 135 and a standard deviation of
12. What percentage of the games that Nayeli bowls does
she score less than 128, to the nearest tenth?

Answer 1

Using the normal distribution, it is found that she scores less than 128 in 28.1% of her games.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the mean and the standard deviation are given, respectively, by $\mu = 135, \sigma = 12$.

The proportion of games in which she scores less than 128 is the p-value of Z when X = 128, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{128 - 135}{12}$

Z = -0.58

Z = -0.58 has a p-value of 0.281.

She scores less than 128 in 28.1% of her games.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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