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Distribution of sample average, variability of distribution

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October 1st, 2022

Suppose investigators are interested in a population of patients who have been recently diagnosed with a particular kind of colon cancer (nonpolypoid colorectal neoplasm). They believe the diameter of the colon cancer lesion at first diagnosis in this particular population is 15.9mm with standard deviation 10.2mm . Let x= lesion diameter for a patient with colon cancer at first diagnosis.
Investigators select a sample 165 patients at random from this population and calculate the average lesion diameter, x , for the sample.

8. How is the sample average, x , distributed? Choose the most likely answer:
a) the distribution of x is exactly binomial
b) the distribution of x is approximately binomial
c) the distribution of x can’t be determined unless we know that x is distributed normally
d) the distribution of x is approximately normal
e) the distribution of x must be the same as the distribution of x

9. Which of the following is true, concerning the variability of the distribution of x (the individual lesion diameter) and the distribution of x (the average lesion diameter in the sample)?
a) x (the individual lesion diameter) varies less than x (the average lesion diameter)
b) x (the individual lesion diameter) varies more than x (the average lesion diameter)
c) x (the individual lesion diameter) varies about the same as x (the average lesion diameter)
d) we need more information to determine which (x or x ) varies more

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