Question 740842: in this problem we test the effectiveness of a serum on curing cattle of a particular virus. The normal rate of infection of the virus in cattle is 25%. (P=.25)
a. on a ranch with 10 steer all are injected with serum. It is observed that none of the steers are infected. Assuming the serum does not work (meaning the infection rate stays the same) What is the probability that none of the 10 are infected?
b. What is the mean and standard deviation for the distribution in part A.
c. On a second ranch with 17 steer all are injected with the serum. It was observed that one seer was infected. Assuming the serum does not work (meaning the infection rate stays the same) what is the probability of having at most one infected steer.
d. What is the mean and standard deviation for the distribution in part c.
e. Which test gives stronger proof of the effectiveness of the serum?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! in this problem we test the effectiveness of a serum on curing cattle of a particular virus. The normal rate of infection of the virus in cattle is 25%. (P=.25)
a. on a ranch with 10 steer all are injected with serum. It is observed that none of the steers are infected. Assuming the serum does not work (meaning the infection rate stays the same) What is the probability that none of the 10 are infected?
P(x = 0) = 0.75^10 = 0.0563
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b. What is the mean and standard deviation for the distribution in part A.
mean = np = 10*0.25 = 2.5
std = sqrt(npq) = sqrt(2.5*0.75) = 1.3693
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c. On a second ranch with 17 steer all are injected with the serum. It was observed that one seer was infected. Assuming the serum does not work (meaning the infection rate stays the same) what is the probability of having at most one infected steer.
P(0<= x <=1) = binomcdf(17,0.25,1) = 0.0501
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d. What is the mean and standard deviation for the distribution in part c.
mean = np = 17*0.25 = 4.25
std = sqrt(npq) = sqrt(4.25*0.75) = 1.7854
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e. Which test gives stronger proof of the effectiveness of the serum?
A larger sample provides more information.
Cheers,
Stan H.
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