A normal distribution has a mean of 50 and standard deviation of 5. Which value produces a negative z-score?

Question

asked Dec 9, 2020 113k views

1 Answer

Felix TheCat · Answer 1 · 2020-12-14T02:01:18+0000

Answer:

$x\:<\:50$ .

Explanation:

The z-score for a normal distribution is calculated using the formula:

$Z=(x-\mu)/(\sigma)$ .

From the question, the distribution has a mean of 50.

$\implies \mu=50$ and the standard deviation is
$\sigma=5$ .

For a z-score to be negative, then,
$(x-\mu)/(\sigma)\:<\:0$ .

$(x-50)/(5)\:<\:0$ .

$x-50\:<\:0* 5$ .

$x-50\:<\:0$ .

$x\:<\:0+50$ .

$\therefore x\:<\:50$ .

Any value less than 50 will produce a negative z-score