The SAT test scores have an average value of 1200 with a standard deviation of 6
ID: 3242524 • Letter: T
Question
The SAT test scores have an average value of 1200 with a standard deviation of 60. A random sample of 40 scores is selected for study.
A) What is the shape, mean(expected value) and standard deviation of the sampling distribution of the sample mean for samples of size 40?
B) What is the probability that the sample mean will be larger than 1220?
C) What is the probability that the sample mean will fall within 10 points of the population mean?
D) What is the probability that the sample mean will be less than 1175?
Explanation / Answer
ans=
A)
The sample is large enough. That is it is greater than 30. Therefore it is enough for the sample to also assume a normal distribution.
Mean =1200
Standard deviation =60/40
=9.4868
B)
=z=(x-bar-µ)/s
=(1220-1200)/9.4868
=2.108
P(z<2.108)=0.9826
P(z>2.108)=1-p(z<2.108)=1-0.9826
=0.0174
C)
This is the probability of having 10 margin of error
P(x<1210)-p(x<1190)
=(1210-1200)/9.4868
=1.054
(1190-1200)/9.4868
=-1.054
P(-1.054<z<1.054)=0.8531-0.1469
=0.7062
D) What is the probability that the sample mean will be less than 1175?
(1175-1200)/9.4868
=25/9.4868
=2.6352
P(z<2.6352)
=0.9959
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