Question

The mean number wins of a team is 37 wins that is normally distributed. The standard deviation is 3 wins. What would be the sections that are one standard deviation from the mean? Select all that apply.
31
34
37
40
43

Answer 1

Using the normal distribution, it is found that the sections that are one standard deviation from the mean are 34 and 40.

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.

The mean and the standard deviation are given, respectively, by:

$\mu = 37, \sigma = 3$

The measures that are one standard deviation from the mean are given by X when Z = -1 and Z = 1, hence:

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

$-1 = \frac{X - 37}{3}$

X - 37 = -3

X = 34

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

$1 = \frac{X - 37}{3}$

X - 37 = 3

X = 40

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

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