Question

a set of test scores is normally distributed with a mean of 75 and a standard deviation of 10. what is the probability that a randomly selected score is more than 85? the z - score is calculated as $z=\frac{(raw score - mean)}{standard deviation}$. test scores. the z - score for 85 is calculated as z = - 2. the area to the right of z=-2 under the normal curve is approximately 15.73%. so, the probability that a randomly selected score is more than 85 is about 15.73%. the z - score for 85 is calculated as z = 1. the area to the right of z = 1 under the normal curve is approximately 15.73%. so, the probability that a randomly selected score is more than 85 is about 15.73%. the z - score for 85 is calculated as z = - 1. the area to the right of z=-1 under the normal curve is approximately 15.73%. so, the probability that a randomly selected score is more than 85 is about 15.73%. the z - score for 85 is calculated as z = 2. the area to the right of z = 2 under the normal curve is approximately 15.73%. so, the probability that a randomly selected score is more than 85 is about 15.73%.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{\text{raw score}-\text{mean}}{\text{standard deviation}}$. Given that the raw score is 85, the mean is 75, and the standard deviation is 10. So, $z=\frac{85 - 75}{10}=\frac{10}{10}=1$.

Step2: Find the area to the right of the z - score

The total area under the normal curve is 1. The area to the left of $z = 1$ can be found from the standard normal distribution table, which is approximately 0.8413. The area to the right of $z=1$ is $1 - 0.8413=0.1573$ or 15.73%.

Answer:

The z - score for 85 is calculated as $z = 1$. The area to the right of $z = 1$ under the normal curve is approximately 15.73%. So, the probability that a randomly selected score is more than 85 is about 15.73%.