Question

The exam scores for 200 students are normally distributed with a mean of 72 and a standard deviation of 10. Which answer choice below represents the number of students with scores between 72 and 82?.

Answer 1

Using the normal distribution, it is found that there are 68 students with scores between 72 and 82.

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:

$\mu = 72, \sigma = 10$

The proportion of students with scores between 72 and 82 is the p-value of Z when X = 82 subtracted by the p-value of Z when X = 72.

X = 82:

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

$Z = \frac{82 - 72}{10}$

Z = 1

Z = 1 has a p-value of 0.84.

X = 72:

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

$Z = \frac{72 - 72}{10}$

Z = 0

Z = 0 has a p-value of 0.5.

0.84 - 0.5 = 0.34.

Out of 200 students, the number is given by:

0.34 x 200 = 68 students with scores between 72 and 82.

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

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