Based on prior experience with thousands of men who do not have prostate cancer,

Question

Based on prior experience with thousands of men who do not have prostate cancer, it can be assumed that the hormone, H5, follows a gaussian distribution with mean 125 mg and standard deviation 7 mg. Further suppose that a man is suspected of having prostate cancer and is referred for biopsy of the prostate, if his H5 level is greater than 140 mg. Explain, using a statistical argument, why some normal, healthy men will have H5 levels greater than 140 (even though they don't have prostate cancer). If a random sample of 112 normal, healthy men is selected, about how many would you expect to be incorrectly suspected of having prostate cancer?

Explanation / Answer

A)

This is because of the variation in the H5 levels of normal, healthy men. Hence, some few of them will have H5 level greater than 140 even though they don't have prostate cancer.

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b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    140      
u = mean =    125      
          
s = standard deviation =    7      
          
Thus,          
          
z = (x - u) / s =    2.142857143      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.142857143   ) =    0.016062286

Hence, around 0.0161*112 = 1.8. [ANSWER]

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