Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- 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:
[tex]\mu = 37, \sigma = 3[/tex]
The measures that are one standard deviation from the mean are given by X when Z = -1 and Z = 1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1 = \frac{X - 37}{3}[/tex]
X - 37 = -3
X = 34
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1 = \frac{X - 37}{3}[/tex]
X - 37 = 3
X = 40
More can be learned about the normal distribution at https://brainly.com/question/24663213
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