Question

a normal distribution has a mean of 85 and a standard deviation of 10. find the z - score for a data value of 103. round to two decimal places question help: video submit question

Explanation:

Step1: Recall the z - score formula

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

Step2: Substitute the given values into the formula

Given \(\mu = 85\), \(\sigma=10\), and \(x = 103\). Then \(z=\frac{103 - 85}{10}\).

Step3: Calculate the numerator

\(103-85 = 18\). So \(z=\frac{18}{10}\).

Step4: Perform the division

\(\frac{18}{10}=1.80\)

Answer:

\(1.80\)