question 7 of 10\nin the class of 2019, more than 1.6 million students took the sat. the distribution of…

question 7 of 10\nin 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.\nwhat proportion of students earned scores between 500 and 600 on the sat math test?\nround your answer to 4 decimal places.

question 7 of 10\nin 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.\nwhat proportion of students earned scores between 500 and 600 on the sat math test?\nround your answer to 4 decimal places.

Answer

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 500$, $z_1=\frac{500 - 528}{117}=\frac{- 28}{117}\approx - 0.24$. For $x = 600$, $z_2=\frac{600 - 528}{117}=\frac{72}{117}\approx0.62$.

Step2: Use the standard normal table

We want to find $P(-0.24<Z<0.62)$. We know that $P(-0.24<Z<0.62)=P(Z < 0.62)-P(Z < - 0.24)$. From the standard - normal table, $P(Z < 0.62)=0.7324$ and $P(Z < - 0.24)=0.4052$. So $P(-0.24<Z<0.62)=0.7324 - 0.4052=0.3272$.

Answer:

$0.3272$