Lightning strikes, continued. The number of lightning strikes on a square kilome

Question

Lightning strikes, continued. The number of lightning strikes on a square kilometre of open ground in a year has mean 6 and standard deviation 2.4. What is the probability that the average number of lightning strikes per square kilometre per year for 25 randomly chosen square kilometres is 4.8 or less? Heights of male students, continued. Suppose that the distribution of heights of all male students on your campus is Normal with mean 70 inches and standard deviation 2.8 inches. What standard deviation must x^bar within 0.5 inch of mu^bar? (Use the 68-95-99.7 rule.) How large an SRS do you need to reduce the standard deviation of x^bar to the value you found in (a)? Glucose testing. Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if her glucose level above 140 milligrams per decilitre (mg/dl) one hour after ingesting a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with mu = 125 mg/dl and sigma = 10 mg/dl. If a single glucose measurement is made, what is the probability that Shelia is diagnosed as having gestational diabetes? If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes?

Explanation / Answer

(a)

z = (140 125)/10 =1.5

P(x >140) = P(z >1.5) = 1- P(z<=1.5)=1-0.93319=0.06681

(b)

z = (140 125)/10/4^0.5 = 3

P(x >140) = P(z > 3) =1-0.99865=0.00135

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