Question

formula 0.5 points
for a normally distributed data set with a mean of 85 and a standard deviation of 8.8, calculate the z - score for a data point of 63.
round your answer to the nearest tenth.
answer

Explanation:

Step1: Recall the z - score formula

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

Step2: Substitute the given values into the formula

Given \(x = 63\), \(\mu=85\), and \(\sigma = 8.8\). Then \(z=\frac{63 - 85}{8.8}\).

Step3: Calculate the numerator

\(63-85=-22\). So the formula becomes \(z=\frac{-22}{8.8}\).

Step4: Perform the division

\(\frac{-22}{8.8}=- 2.5\)

Answer:

\(-2.5\)