Respuesta :
Answer:
7.44 is the answer
Step-by-step explanation:
Using the normal distribution, it is found that this value was 7.5 points below the average.
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.
In this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 22.5, \sigma = 6.2[/tex].
In one game, the number of points the athlete scored was 1.2 standard deviations below his mean, hence Z = -1.2 and the score was of X, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.2 = \frac{X - 22.5}{6.2}[/tex]
X - 22.5 = -1.2 x 6.2
X = 15.
15 - 22.5 = 7.5.
This value was 7.5 points below the average.
More can be learned about the normal distribution at https://brainly.com/question/24663213
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