Respuesta :
Using the normal distribution, it is found that there was a 0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
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 = 700, \sigma = 50[/tex].
The probability of a month having a PCE between $575 and $790 is the p-value of Z when X = 790 subtracted by the p-value of Z when X = 575, hence:
X = 790:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{790 - 700}{50}[/tex]
Z = 1.8
Z = 1.8 has a p-value of 0.9641.
X = 575:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{575 - 700}{50}[/tex]
Z = -2.5
Z = -2.5 has a p-value of 0.0062.
0.9641 - 0.0062 = 0.9579.
0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
More can be learned about the normal distribution at https://brainly.com/question/4079902
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