Respuesta :
Using the normal distribution, it is found that she scores less than 192 in 99.3% of games.
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, the mean and the standard deviation are given, respectively, by [tex]\mu = 160, \sigma = 13[/tex].
The proportion of games in which she scores less than 192 is the p-value of Z when X = 192, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{192 - 160}{13}[/tex]
[tex]Z = 2.46[/tex]
[tex]Z = 2.46[/tex] has a p-value of 0.993.
Hence, she scores less than 192 in 99.3% of games.
More can be learned about the normal distribution at https://brainly.com/question/24663213
