Using the normal distribution, it is found that the correct option is 0.8185946784.
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Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula, which in a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], for a measure X, is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of measure X.
The proportion of measures between [tex]\mu - 2\sigma[/tex] and [tex]\mu + \sigma[/tex] is the p-value of Z when [tex]X = \mu + \sigma[/tex] subtracted by the p-value of Z when [tex]X = \mu - 2\sigma[/tex]. Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{\mu + \sigma - \mu}{\sigma}[/tex]
[tex]Z = \frac{\sigma}{\sigma}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{\mu - 2\sigma - \mu}{\sigma}[/tex]
[tex]Z = \frac{-2\sigma}{\sigma}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.8413 - 0.0228 = 0.8185.
Thus, the correct option is 0.8185946784.
A similar problem is given at https://brainly.com/question/24841527
