SOLUTION: It is estimated that approximately 3 percent of the population is affected with the virus that causes HIV. In a random sample of 100 persons calculate;
a. less than 2 percent are
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Question 520781: It is estimated that approximately 3 percent of the population is affected with the virus that causes HIV. In a random sample of 100 persons calculate;
a. less than 2 percent are affected
b. between 2 percent and 4 percent
c. no less than 2 percent of persons are affected
d. 3 percent of persons are affected
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It is estimated that approximately 3 percent of the population is affected with the virus that causes HIV. In a random sample of 100 persons calculate;
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p = 0.03 ; q = 0.97
std for groups of 100 = sqrt[pq/n] = sqrt[0.03*0.97/100] = 0.0171
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a. less than 2 percent are affected
z(0.02) = (0.02-0.03)/0.0171 = -0.5862
P(p-hat< 0.02) = P(z < -0.5862) = 0.2789
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b. between 2 percent and 4 percent
z(0.04) = (0.04-0.03)/0.0171 = +0.5862
P(0.02 < phat < 0.04) = P(-0.5862< z < +0.5862) = 0.4423
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c. no less than 2 percent of persons are affected
P(phat >= 0.02) = P(z >= -0.5862) = 0.7211
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d. 3 percent of persons are affected
P(phat = 0.03) = 0
Why? The probability of ANY particular value
in a continuous distribution is zero.
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Cheers,
Stan H.
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