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 (z) is the z - score, (x) is the data item, (\mu) is the mean, and (\sigma) is the standard deviation.

Step2: Substitute the given values into the formula

We are given that (\mu = 20), (\sigma=5), and (z = 1.5). Substituting these into the formula (z=\frac{x-\mu}{\sigma}), we get (1.5=\frac{x - 20}{5}).

Step3: Solve for (x)

Multiply both sides of the equation (1.5=\frac{x - 20}{5}) by (5): (1.5\times5=x - 20). So, (7.5=x - 20). Then add (20) to both sides: (x=20 + 7.5).

Answer:

(27.5)