Question 1192872: The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean = 548.4 and standard deviation = 28.1 .
(a) What is the probability that a single student randomly chosen from all those taking the test scores 553 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 x
, of 35 students?
The mean of the sampling distribution for x
is:
The standard deviation of the sampling distribution for
is:
(c) What z-score corresponds to the mean score x
of 553?
ANSWER:
(d) What is the probability that the mean score x
of these students is 553 or higher?
ANSWER:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
z>(553-548.4)/28.1=0.1637
probability z > 0.1637 is 0.4350
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for 35 students, the mean of the sampling distribution is 548.4, no change.
the sd is original sd/sqrt(n)=4.75
-
z now is 4.6/4.75=0.97
the probability now is 0.1664
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