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Sagot :
Using the normal distribution, the value of z is of z = 1.5.
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.
For this problem, considering the symmetry of the normal distribution, the area above the mean is given by:
0.8664/2 = 0.4332.
Hence z has a p-value of 0.5 + 0.4332 = 0.9332, hence the value of z is z = 1.5.
More can be learned about the normal distribution at https://brainly.com/question/24537145
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