Almost 1.5 million college-bound high school seniors took the Critical Reading p

Question

Almost 1.5 million college-bound high school seniors took the Critical Reading portion of the SAT exam recently. The mean was 503; the standard deviation was 113.

a. What proportion scored 500 or above?
b. Suppose that a university, based on past experience, decided to not admit anyone whose Critical Reading score placed them in the lowest 20 percent of the population. What is that score?
c. What proportion of the population scored between 600 and 700?
d. From 1000 students, how many would be expected to score 700 or more?
e. In working these problems, you began with an assumption about the distribution of Critical Reading test scores. What is that assumption?

Explanation / Answer

a) From information given, Xi=500, Xbar=503 and s=113. Substitute the values in following equation to obtain the z score.

z=(Xi-Xbar)/s=(500-503)/113=-0.03; Find area corresponding to -0.03, this gives the required proportion. 0.4880 [ans]

b) From iinformation, z=0.20, Xbar=503, s=113. Substitute the values in z score equation to obtain the Xi.

0.20=(Xi-503)/113

Xi=525.6~526.

c) Find z score scorresponding to Xi=600 nd 700 respectively.

z1=(600-503)/113=0.86 and z2=(700-503)/113=1.74

Find areas corresponding to 0.86 and 1.74. Subtract the smaller from the larger. [0.4591-0.3051=0.154 (ans)]

d) ci=Xbar+-z(s/sqrt n)=503+-1.96(113/sqrt1000)=503+-7=496 to 510

Between 496 and 510 students are expected to score above 700.

e) The sampling distribution of sample means is normal with high sample size.

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