of the Scholastic Aptitude Test 2009): Critical Reading Mathematics Writing 502
ID: 3329752 • Letter: O
Question
of the Scholastic Aptitude Test 2009): Critical Reading Mathematics Writing 502 515 494 Assume that the population standard deviation on each part of the test is = 100 a. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places. b. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places. what is the probability a sample of 100 test takers will provide a sample mean test score within 10 of the population mean ofs decimals)? c on the ting a ofthe test Round z value in intermediate calculation to 2 decimals places.Explanation / Answer
Solution:
a) Population mean = 502
Sample size n = 90
Population SD = 100
SD of X bar = 100/sqrt(90)
=10.5410
normal distribution with mean 502, SD 10.5410
P(492 < x < 512)
Z = 10/10.5410
Z = 0.9487, -0.9487
P(z < 0.9487) – P(z < -0.9487)
= 0.8289-0.1711
= 0.6578
b) SD x bar = 10.5410
Z = 10/10.5410
Z = 0.9487, -0.9487
P(z < 0.9487) – P(z < -0.9487)
0.8289-0.1711
= same values as (a)
=0.6578
probability is the same.
c) 100/sqrt(10)
SD = 10
10/10 = 1
P(-1 < z < 1)
= P(z < 1)-P( z < -1) = 0.6862
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