Question

A normal distribution has a mean of 101 and a standard deviation of 3.4. What is the z-score of 105? Enter your answer, rounded to the nearest hundredth, in the box.

Answer 1

Answer:

Z-score = 1.18

Step-by-step explanation:

The z-score measures how many standard deviations from the mean a data is

Therefore the z score is the quotient between the difference between a value and the mean and the standard deviation

$Z =\frac{X-\mu}{\sigma}$

Where

μ is the mean, x is a data of the population and $\sigma$ is the standard deviation

In this case

$\mu =101\\\\\sigma = 3.4\\\\X = 105$

Then the z-score is

$Z = \frac{105-101}{3.4}\\\\Z = 1.18$