act scores are normally distributed with a mean of 20 and standard deviation 5. find the data item in this…

Explanation:

Step1: Recall the z - score formula

The z - score formula is (z=\frac{x-\mu}{\sigma}), where (x) is the data item, (\mu) is the mean, and (\sigma) is the standard deviation. We need to solve for (x).

Step2: Rearrange the formula for (x)

Multiply both sides of (z = \frac{x-\mu}{\sigma}) by (\sigma): (z\sigma=x - \mu). Then add (\mu) to both sides: (x=\mu+z\sigma).

Step3: Substitute the given values

Given (\mu = 20), (z = 1.5), and (\sigma=5). Substitute into (x=\mu+z\sigma): (x = 20+(1.5\times5)).

Step4: Calculate the value of (x)

First, calculate (1.5\times5 = 7.5). Then (x=20 + 7.5).

Answer:

(27.5)