Question

On a test, mean score was 70 and the standard deviation of the scores was 15.

Answer 1

Answer:

$P(x\:$

Step-by-step explanation:

To  find the probability that a randomly selected test taker scored below 50, we need to first of all determine the z-score of 50.

The z-score for a normal distribution is given by:

$z=\frac{x-\bar x}{\sigma}$.

From the question, the mean score is $\bar x=70$, the standard deviation is, $\sigma=15$, and the test score is $x=50$.

We substitute these values into the formula to get:

 $z=\frac{50-70}{15}$.

 $z=\frac{-20}{15}=-1.33$.

We now read the area that corresponds to a z-score of -1.33 from the standard normal distribution table.

From the table, a z-score of -1.33 corresponds to and area of 0.09176.

Therefore the probability that a randomly selected test taker scored below 50 is $P(x\:$