1. The SAT test scores have an average value of 1200 with a standard deviation o

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Question

1. 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 1225?

C) What is the probability that the sample mean will fall within 5 points of the population mean?

D) What is the probability that the sample mean will be less than 1180?

Mean = 1200

Sd = 60

n = 40

A) shape of distribution is bell shaped.

Mean of sample mean = 1200

Sd of sample mean = sd/sqrt (n) = 60/sqrt (40) = 9.49

B) P(X bar > 1225) = P(Z > (1225-1200)/9.49)

= P(Z > 2.63)

= 1 - P(Z < 2.63)

= 1 - 0.9957

= 0.0043

C) Probability = P(-5/9.49 < Z < 5/4.9)

= P(-0.53 < Z < 0.53)

= P(Z < 0.53) - P(Z < - 0.53)

= 0.7019 - 0. 2981

= 0.4038

D) P(X bar < 1180) = P(Z < (1180 - 1200)/9.49)

= P(Z < - 2.11)

= 0.0174

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