4. the average height of students is 65 inches with a standard deviation of 3 inches.\na. find the z - score…

Explanation:

Step1: Recall the z - score formula

The z - score formula is (z=\frac{x-\mu}{\sigma}), where (x) is the data point, (\mu) is the mean, and (\sigma) is the standard deviation. Given (\mu = 65), (\sigma=3), and (x = 70).

Step2: Substitute the values into the formula

Substitute (x = 70), (\mu = 65), and (\sigma = 3) into (z=\frac{x-\mu}{\sigma}). [ \begin{align*} z&=\frac{70 - 65}{3}\ &=\frac{5}{3}\approx1.67 \end{align*} ]

Step3: Interpret the z - score

A z - score of (z\approx1.67) means that the student's height of 70 inches is approximately (1.67) standard deviations above the mean height of 65 inches.

Answer:

a. The z - score is (\frac{5}{3}\approx1.67). b. The student's height of 70 inches is approximately (1.67) standard deviations above the mean height of 65 inches.