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 1008 and standard deviation of 219. 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: 0.0035

Step-by-step explanation:

Given : The  distribution of SAT scores of combining mathematics and reading was approximately Normal with mean of $\mu=1008$ and standard deviation of $\sigma=219$.

Let x be a random variable that represents the SAT scores of combining mathematics and reading.

Using formula , $z=\dfrac{x-\mu}{\sigma}$, the z-value corresponds x= 1600 will be

$z=\dfrac{1600-1008}{219}\approx2.70$

Now using the standard normal table for z, we get

The probability that SAT scores were actually higher than 1600 will be :-

$P(x>1600)=P(z>2.70)=1-P(z$ [Rounded to 4 decimal places.]

Since scores 1600 and above are reported as 1600.

Thus, the proportion of SAT scores for the combined portions were reported as 1600 = 0.0035