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

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asked Jan 24, 2019 12.4k views

1 Answer

Dale Hagglund · Answer 1 · 2019-01-28T14:51:03+0000

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,
$\sigma^(2)=25$

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

=√(25)

The z-score formula is given below:

$z=(x-\mu)/(\sigma)$

=(110-100)/(5)

=(10)/(5)

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

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