SOLUTION: A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is: a. Less than 74. b. Between 74 and 76.

Algebra ->  Probability-and-statistics -> SOLUTION: A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is: a. Less than 74. b. Between 74 and 76.      Log On


   

Question 342479: A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is:
a. Less than 74.
b. Between 74 and 76.
c. Between 76 and 77.
d. Greater than 77.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A normal population has a mean of 75 and a standard deviation of 5.
You select a sample of 40. Compute the probability the sample mean is:
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Note: The mean of the sample means is 75
The std of the sample means is 5/sqrt(40) = 0.7906
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a. Less than 74.
t(74) = (74-75)/0.7906 = -1.2649
P(xbar < 74) = P(t < -1.2649 when df = 39) = 0.1067
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b. Between 74 and 76.
t(76) = (76-75)/0.7906 = +1.2649
P(74< xbar < 76) = P(-1.2649 < t < 1.2649 when df = 39) = 0.7866
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c. Between 76 and 77.
d. Greater than 77.
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Use the same procedure for "c" and for "d".
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Cheers,
Stan H.