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Renal Disease 

The presence Of bacteria in a urine sample (bacteriuria) is 

sometimes associated with symptoms of kidney disease in 

women. Suppose a determination of bacteriuria has been 

made over a large population Of women at one point in 

time and 5% of those sampled are positive for bacteriuria. 

4.33 If a sample size of 5 is selected from this population, 

what is the probability that 1 Or more women are positive for 

bacteriuria? 

4.34 Suppose 100 women from this population are sam- 

pled. What is the probability that 3 Or more Of them are 

positive for bacteriuria? 

One interesting phenomenon of bacteriuria is that there is 

a "turnover"; that is, if bacteriuria is measured on the same 

woman at two different points in time, the results are not 

necessarily the same. Assume that 20% of all women who 

are bacteriuric at time O are again bacteriuric at time I 

(1 year later), whereas only 4.2% Of women who were not 

bacteriuric at time O are bacteriuric at time 1. Let X be the 

random variable representing the number of bacteriuric 

events over the two time periods for 1 woman and still as- 

Sume that the probability that a woman will be positive for 

bacteriuria at any one exam is 5%. 

4.35 What is the probability distribution Of X? 

4.36 What is the mean Of X? 

4.37 What is the variance of X? 

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