Question

last year 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 to 4 decimal places.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score 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 distribution

We want to find \(P(X\lt350)\), which is equivalent to \(P(Z\lt - 1.5214)\) using the standard normal distribution \(Z\sim N(0,1)\).
Looking up the value in the standard normal table (or using a calculator with a normal - distribution function, e.g., in R: pnorm(-1.5214) or in Excel: NORM.S.DIST(-1.5214,TRUE)), we get \(P(Z\lt - 1.5214)\approx0.0642\)

Answer:

\(0.0642\)