Question

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

Answer 1

Answer:

$x\:<\:50$.

Step-by-step explanation:

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

$Z=\frac{x-\mu}{\sigma}$.

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, $\frac{x-\mu}{\sigma}\:<\:0$.

$\frac{x-50}{5}\:<\:0$.

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

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

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

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

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