SOLUTION: 6.The scores for an admissions test have a mean of 1200 with a standard deviation of 60. A random sample of 64 scores is selected and the sample mean is calculated. a)The sample

Question 615851: 6.The scores for an admissions test have a mean of 1200 with a standard deviation of 60. A random sample of 64 scores is selected and the sample mean is calculated.
a)The sample mean is Normally distributed. What are the mean and the standard deviation for the distribution of the sample mean?
b)What is the probability that the sample mean will be larger than 1205?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The scores for an admissions test have a mean of 1200 with a standard deviation of 60. A random sample of 64 scores is selected and the sample mean is calculated.
a)The sample mean is Normally distributed. What are the mean and the standard deviation for the distribution of the sample mean?
The Central Limit Theorem says:
The mean of the sample means = the mean of the population: 1200
The std of the sample means = 60/sqrt(64) = 60/8 = 7.5
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b)What is the probability that the sample mean will be larger than 1205?
z(1205) = (1205-1200)/7.5 = 2/3
P(x-bar > 1205) = P(z > 2/3) = normalcdf(2/3,100) = 0.2525
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Cheers,
Stan H.
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