Set the mean and standard deviation to 0 and 5 , respectively. Approximately 5% of the area under the normal curve lies to the right of 8.2 . Consider what would happen if you were to change the mean to 50 and keep the standard deviation at 5 . Can you predict the new value for which approximately 5% of the area under the normal curve lies to the right of this value? Enter your answer accurate to one decimal place.

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joaobezerra joaobezerra · Answer 1 · 2021-10-27T12:20:29+02:00

Using z-scores and the normal distribution, it is found that the new value would be of 58.2.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It 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 X, which is the area to the left of Z under the normal curve.
The area to the right of Z is 1 subtracted by the p-value of Z.

In this problem:

Mean of 50 and standard deviation of 5, thus [tex]\mu = 50, \sigma = 5[/tex].
Area to the right of 0.05, thus Z with a p-value of 1 - 0.05 = 0.95, thus [tex]Z = 1.645[/tex].

We have to find the value of X, then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 50}{5}[/tex]

[tex]X - 50 = 1.645(5)[/tex]

[tex]X = 58.2[/tex]

A similar problem is given at https://brainly.com/question/15583760