Question

in a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.5. answer parts (a)-(d) below. (a) find the probability that a randomly selected medical student who took the test had a total score that was less than 487. the probability that a randomly selected medical student who took the test had a total score that was less than 487 is (round to four decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 487$, $\mu=500$, and $\sigma = 10.5$.
$z=\frac{487 - 500}{10.5}=\frac{- 13}{10.5}\approx - 1.24$

Step2: Find the probability

We use the standard normal distribution table (or z - table) to find $P(Z\lt - 1.24)$. Looking up the value in the z - table, we get $P(Z\lt - 1.24)=0.1075$

Answer:

$0.1075$