Answer:
For a height of 66 inches, Z = 0.65.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average height was about 64.3 inches; the SD was about 2.6 inches.
This means that [tex]\mu = 64.3, \sigma = 2.6[/tex]
66 inches:
The z-score for a height of 66 inches is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66 - 64.3}{2.6}[/tex]
[tex]Z = 0.65[/tex]
For a height of 66 inches, Z = 0.65.
