Question

a set of data items is normally distributed with a mean of 200 and a standard deviation of 60. find the data item in this z = 1.5 the data item that corresponds to z = 1.5 is (type an integer or a decimal.)

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 to solve 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 \(\mu = 200\), \(z = 1.5\), and \(\sigma=60\). Substitute these values into the formula \(x=\mu+z\sigma\): \(x = 200+1.5\times60\).

Step4: Calculate the value of \(x\)

First, calculate \(1.5\times60 = 90\). Then \(x=200 + 90\).

Answer:

\(290\)