Question

a set of data items is normally distributed with a mean of 855 and a standard deviation of 16. find the data item in this distribution that corresponds to the given z-score.
( z=-6 )
the data item that corresponds to ( z=-6 ) 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 value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. We need to solve for \(x\).

Step2: Rearrange the formula for \(x\)

From \(z = \frac{x-\mu}{\sigma}\), we can get \(x=\mu+z\sigma\).

Step3: Substitute the given values

Given \(\mu = 855\), \(z=-6\), and \(\sigma = 16\). Then \(x=855+(-6)\times16\).
First, calculate \((-6)\times16=-96\).
Then \(x = 855-96\).

Step4: Compute the value of \(x\)

\(x=759\).

Answer:

\(759\)