Question

SAT math scores for a particular year are normally distributed with a mean of 510 and a standard deviation of 80.

What is the probability that a randomly selected score is greater than 590? Enter the numerical answer only (no percent sign).

Answer 1

Using the normal distribution, it is found that there is a 16% probability that a randomly selected score is greater than 590.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the mean and the standard deviation are, respectively, given by $\mu = 510$ and $\sigma = 80$.

The probability that a randomly selected score is greater than 590 is one subtracted by the p-value of Z when X = 590, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{590 - 510}{80}$

Z = 1

Z = 1 has a p-value of 0.84.

1 - 0.84 = 0.16.

0.16 = 16% probability that a randomly selected score is greater than 590.

More can be learned about the normal distribution at https://brainly.com/question/24663213