Question

It is possible to score higher than 1600 on the combined mathematics and reading portions of the SAT, but scores 1600 and above are reported as 1600. Suppose the distribution of SAT scores (combining mathematics and reading) was approximately Normal with mean of 1003 and standard deviation of 220. What proportion of SAT scores for the combined portions were reported as 1600? That is, what proportion of SAT scores were actually higher than 1600? (Enter an answer rounded to four decimal places.)

Answer 1

Answer: 0.0034

Step-by-step explanation:

Given : The distribution of SAT scores (combining mathematics and reading) was approximately Normal with $\mu=1003$ and $\sigma=220$

let x be the random variable that represents the SAT scores.

Using formula $z=\dfrac{x-\mu}{\sigma}$, the value of z corresponding to 1600 will be :-

$z=\dfrac{1600-1003}{220}=\dfrac{597}{220}\approx2.71$

By using the standard normal table , we have

The proportion of SAT scores were actually higher than 1600 will be :-

$P(z>2.71)=1-P(z\leq2.71)\\\\=1- 0.9966358=0.0033642\approx0.0034$

Hence, the proportion of SAT scores for the combined portions were reported as 1600 = 0.0034