The scores of individual students on the American College Testing (ACT) composit
ID: 3358340 • Letter: T
Question
The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with mean 19.4 and standard deviation 5.3 (a) What is the probability that a single student randomly chosen from all those taking the test scores 28 or higher? (b) Now take an SRS of 58 students who took the test. What are the mean and standard deviation of the average (sample mean) score for the 58 students? = Do your results depend on the fact that individual scores have a normal distribution? O yes O no (c) What is the probablity that the mean score x of these students is 20.46 or higher?Explanation / Answer
Mean = 19.4
Sd = 5.3
A) P(X > 28) = P(Z > (28 - 19.4)/5.3)
= P(Z > 1.62)
= 1 - P(Z < 1.62)
= 1 - 0.9474
= 0.0526
B) n = 58
Mean of sampling distribution = 19.4
Standard deviation of sampling distribution = 5.3/sqrt(58) = 0.70
Option-B) No
C) P(X bar > 20.46) = P(Z > (20.46 - 19.4)/0.7)
= P(Z > 0.2)
= 1 - P(Z < 0.2)
= 1 - 0.5793
= 0.4207
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