Question

the heights of the students in your class are normally distributed with a mean of 56 inches and a standard deviation of 2 inches. if a z score of 2.70 describes your height, how tall are you in inches? round to two decimal places

Explanation:

Step1: Recall the z - score formula

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

Step2: Rearrange the formula to solve for \(x\)

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

Step3: Substitute the given values

Given \(\mu = 56\), \(z = 2.70\), and \(\sigma=2\). Then \(x=56+(2.70\times2)\).

Step4: Calculate the value of \(x\)

First, calculate \(2.70\times2 = 5.4\). Then \(x=56 + 5.4=61.4\).

Answer:

\(61.40\)