Question

in the class of 2019, more than 1.6 million students took the sat. the distribution of scores on the math section (out of 800) is approximately normal with a mean of 528 and standard deviation of 117. the university of michigan has a recommended sat math score of at least 730. what percent of students who took the sat math test meet this requirement? round your answer to 4 decimal places and then convert to a percentage. %

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 730$ (the score of interest), $\mu = 528$ (mean) and $\sigma=117$ (standard deviation). So, $z=\frac{730 - 528}{117}=\frac{202}{117}\approx1.7265$.

Step2: Find the proportion of data above the z - score

We know that the total area under the normal - distribution curve is 1. Using a standard normal distribution table (or z - table), the proportion of data to the left of $z = 1.7265$ is approximately $0.9586$. The proportion of data to the right of $z$ (students with score at least 730) is $1 - 0.9586=0.0414$.

Step3: Convert to percentage

To convert the proportion to a percentage, we multiply by 100. So, $0.0414\times100 = 4.14\%$.

Answer:

4.14%