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Distribution of sample average, variability of distribution

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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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 ...

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