Question

question 2 of 10 > 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. about what proportion of students who took the sat scored less than 350 on the math section? round your answer to 4 decimal places.

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 350$, $\mu=528$, and $\sigma = 117$.
$z=\frac{350 - 528}{117}=\frac{-178}{117}\approx - 1.5214$

Step2: Find the proportion using the standard normal table

We want to find $P(X\lt350)$, which is equivalent to $P(Z\lt - 1.5214)$ in the standard - normal distribution. Looking up the value in the standard normal table (or using a calculator with a normal - distribution function), we know that the standard normal table gives the cumulative probability for $z$ values.
$P(Z\lt - 1.5214)\approx0.0642$

Answer:

$0.0642$