Using the normal distribution, it is found that the z-score when X = 89 is of 2.63.
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 is of [tex]\mu = 64[/tex].
- The standard deviation is of [tex]\sigma = 9.5[/tex].
The complete question asks the z-score when he types 89 words in a minute, that is, Z when X = 89, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{89 - 64}{9.5}[/tex]
[tex]Z = 2.63[/tex]
More can be learned about the normal distribution at https://brainly.com/question/24663213
