Respuesta :
Using the normal distribution, it is found that his mean number of points in a game is of 27.
Normal Probability Distribution
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], 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.
In this problem, we have that the parameters are as follows:
[tex]\sigma = 4, X = 43, Z = 4[/tex].
We have to solve for the mean [tex]\mu[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]4 = \frac{43 - \mu}{4}[/tex]
[tex]43 - \mu = 16[/tex]
[tex]\mu = 27[/tex]
His mean number of points in a game is of 27.
More can be learned about the normal distribution at https://brainly.com/question/24663213
