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Statistics: Normal Distribution Sample Calculations

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Question 1.
If you have a normal distribution of a random variable x, with a mean of 56 and standard deviation of 8: What is the probability that the random variable x will be within plus or minus 1 standard deviation of the mean?
a. 0.682
b. 0.75
c. 0.00

Question 2
What is the probability that x is greater than 64?
a. 0.190
b. 0.159
c. 0.140

Question 3
What is the probability that x is less than 42?
a. 0.900
b. 0.410
c. 0.0401

Question 4
Refer to this weeks case study. With the 24 means that we accumulated in our survey, we can get a pretty good picture of what kind of money we might be making after a few years. After all, we are certain that the distribution of the sample results (i.e., money spent in the bakery. was normal, which means that the distribution of those means we calculated is also normal. Because we have a sampling distribution, we have a much better idea of the true mean of our income than if we just took the mean of one sample and used it to approximate our income. Find the probability of my income being between $90 and $92 per visit.
a. 0.0468
b. 0.500
c. 0.468

Question 5
Refer to this weeks case study. For the following take the values of the means I got, set them up as a probability distribution (which is normal), and then find the population mean and standard deviation. The mean (µ) turns out to be $85 per visit and the standard deviation (s) $16 per visit. Find the probability of my income being greater than $80 per visit.
a. 0.765
b. 0.890
c. 0.937

Question 6
Refer to this week's case study. Find the probability of my income being less than $89 per visit.
a. 0.900
b. 0.888
c. 0.675

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