The scores of students on the SAT college entrance examinations at a certain hig
ID: 2924543 • Letter: T
Question
The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean =543.4=543.4 and standard deviation =25.4=25.4.
(a) What is the probability that a single student randomly chosen from all those taking the test scores 549 or higher?
ANSWER:
For parts (b) through (d), consider a random sample of 35 students who took the test.
(b) What are the mean and standard deviation of the sample mean score x¯x¯, of 35 students?
The mean of the sampling distribution for x¯x¯ is:
The standard deviation of the sampling distribution for x¯x¯ is:
(c) What z-score corresponds to the mean score x¯x¯ of 549?
ANSWER:
(d) What is the probability that the mean score x¯x¯ of these students is 549 or higher?
ANSWER:
Explanation / Answer
Solution:
a) Given mean = 543.4, standard deviation = 25.4
P(x > 549) = P( z > (549-543.4)/25.4) = 0.22047
b) mean = 534.6
stdev of mean = stdev/sqrt(n) = 25.4/sqrt(35) = 4.29
c) z = (549-543.4)/4.29 = 1.30536
d) P(z > 1.30536) = 1P ( Z<1.30536 )
= 1 0.9049 = 0.0951