/ math 2100 18 / 4/2 Homework6.4: Problem 2 Previous Problem Problem ListNext Pr
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/ math 2100 18 / 4/2 Homework6.4: Problem 2 Previous Problem Problem ListNext Problem (1 point) The scores of students on the SAT ? 559.4 and standard deviation ? 26. entrance examinations at a certain high school had a normal distribution with mean (a) What is the probability that a single student randomly chosen from all those taking the test scores 566 or higher? ANSWER For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test (b) What are the mean and standard deviation of the sample mean score i. of 35 students? The mean of the sampling distribution for ž is The standard deviation of the sampling distribution for t is (c) What z-score corresponds to the mean score i of 566? ANSWER (d) What is the probability that the mean score ANSWER of these students is 566 or higher?Explanation / Answer
Solution:- Given that ? = 559.4, ? = 26
(a) P(X > 566) = P((x-?)/? > (566-559.4)/26)
= P(Z > 0.2538)
= 0.4013
(b) For n = 35
The mean of the sampling distribution for x-bar is 559.4
The standard deviation of the sampling distribution for x-bar is 4.3948
=> 26/sqrt(35) = 4.3948
(c) Z = (x-?)/(?/sqrt(n))
= (566-559.4)/4.3948
= 1.5018
(d) P(X > 566) = P ( Z>1.5018) = 1?P (Z < 1.5018) = 1 ? 0.9332 = 0.0668
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