Question

In that same year, the mean of the math portion of the SAT was 466, with a standard deviation of 117. Keep that in mind to answer the following questions:

a) Some schools use SAT scores for admission. Suppose an engineering school established 600 as the lowest acceptable score for admission. What proportion of the high school seniors would be excluded by such a policy? Draw the picture

b) What proportion of the population would be expected to score between 350 and 550? Draw the picture

c) Some colleges have a fairly stiff math requirement. Suppose the college decided not to admit anyone who was in the bottom 15 percent of the population. What would the cutoff score be? Draw the picture

d) In an urban high school, there were 750 college-bound seniors. How many could be advised to not bother to apply to the school mentioned in A and C above? Draw the picture

e) In working the problems above, you have been making an important assumption about the distribution of math SAT scores. What is that assumption?

Answer 1

a)

Here we need to find the area right to 600 under the normal curve.

Following is the curve:

(b)

Following is the curve:

(c)

Here we need to find the score that have 0.15 area to its left.

Following is the curve:

(d)

Expected number of students scoring below 600 is 1 - 0.1251 = 0.8749

So number of students  could be advised to not bother to apply to the school mentioned in A and C above is

0.8749 * 750 = 656.175

Answer: 656

(e)

Assumption: Distribution of SAT scores in normally distributed.