Question

A random variable x is normally distributed with a mean of 100 and a variance of 25. Given that x = 110, its corresponding z- score is 0.40.
a. True
b. False

Answer 1

A random variable x is normally distributed with a mean of 100 and a variance of 25. Given that x = 110, its corresponding z- score is 0.40.

Answer: The given z-score is false.

Explanation: We are given:

Mean, $\mu=100$,

Variance, $\sigma^{2}=25$

$\therefore\sigma=\sqrt{\sigma^{2}}$

                 $=\sqrt{25}$

                 $=5$

The z-score formula is given below:

$z=\frac{x-\mu}{\sigma}$

        $=\frac{110-100}{5}$

        $=\frac{10}{5}$

        $=2$

Therefore, the z-score corresponding x=100 is 2

Therefore, the given z-score = 0.4 is false.