SOLUTION: A normal population has a mean of $62 and standard deviation of $14. You select random samples of nine.
a. What is the probability that a sample mean is greater than $65? (Round
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a. What is the probability that a sample mean is greater than $65? (Round
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Question 1200796: A normal population has a mean of $62 and standard deviation of $14. You select random samples of nine.
a. What is the probability that a sample mean is greater than $65? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
What is the probability that a sample mean is less than $58? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
What is the probability that a sample mean is between $58 and $65? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
What is the probability that the sampling error ( x¯
− μ) would be $9 or more? That is, what is the probability that the estimate of the population mean is less than $53 or more than $71? (Round z-value to 2 decimal places and final answer to 4 decimal places.) Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! population mean is 62.
population standard deviation is 14.
sample size is 9.
standard error is standard deviation / sqrt(sample size) = 14 / sqrt(9) = 4.66667.
round z-score to 2 decimal places.
round probability to 4 decimal places.
formula to use is z = (x-m)/s
z is the z-score
x is the sample mean
m is the population mean
s is the standard error that was derived from the population standard deviation divided by the square root of the sample size = 4.66667 as shown above.
a. What is the probability that a sample mean is greater than $65? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
What is the probability that a sample mean is less than $58? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
formula becomes z = (58 - 62) / 4.66667 = -4 / 4.66667 = -.86.
area to the left of that = .1949 *****
that's the probbility of getting a z-score less than -.86, which is the same as getting a sample mean less than 58.
What is the probability that a sample mean is between $58 and $65? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
lower limit z = (58 - 62) / 4.66667 = -.86
high limit z = (65 - 62) / 4.66667 = .64
area to the left of z = -.86 = .1949
area to the left of z = .64 = .7389
area in between = .7389 minus .1949 = .5440 *****
that's the probability of getting a z-score between -.86 and .64, whiich is the same as getting a sample mean between 58 and 65.
What is the probability that the sampling error ( x¯
− μ) would be $9 or more? That is, what is the probability that the estimate of the population mean is less than $53 or more than $71? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
area to the left of z = -1.93 = .0268
area to the right of z = 1.93 = .0268
the probability of either getting a z-score less than -1.93 or greater than 1.93 = .0268 + .0268 = .0536. *****
that's the same as getting a sample mean less than 53 or greater than 71.
