Question

the distribution of scores on the sat is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. for the population of students who have taken the sat: what proportion have sat scores less than 400? select what proportion have sat scores greater than 650? select

Explanation:

Step1: Calculate z - score for 400

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 400$, $\mu = 500$, and $\sigma=100$. So $z=\frac{400 - 500}{100}=\frac{- 100}{100}=-1$.

Step2: Find proportion for $z=-1$

Using the standard normal distribution table, the proportion of values to the left of $z = - 1$ is 0.1587.

Step3: Calculate z - score for 650

Using the z - score formula again with $x = 650$, $\mu = 500$, and $\sigma = 100$. So $z=\frac{650 - 500}{100}=\frac{150}{100}=1.5$.

Step4: Find proportion for $z = 1.5$

The proportion of values to the left of $z = 1.5$ from the standard normal distribution table is 0.9332. The proportion of values greater than $z = 1.5$ is $1 - 0.9332=0.0668$.

Answer:

What proportion have SAT scores less than 400? 0.1587
What proportion have SAT scores greater than 650? 0.0668