The survival times of adult mosquitoes exposed to a commonly used synthetic pest

Question

The survival times of adult mosquitoes exposed to a commonly used synthetic pesticide (Phenothrin) follows a gamma distribution with mean time until extermination of 48 seconds and a standard deviation of 15.18 seconds. What is the probability that a random sample of 40 mosquitoes will have an average survival time between 47.5 and 48 seconds? 0.0120 0.0832 0.4880 0.4207 The survival times of adult mosquitoes exposed to a commonly used synthetic pesticide (Phenothrin) follows a gamma distribution with mean time until extermination of 48 seconds and a standard deviation of 15.18 seconds. What is the probability that a random sample of 40 mosquitoes will have an average survival time between 47.5 and 48 seconds? 0.0120 0.0832 0.4880 0.4207

Explanation / Answer

mean = 48

standard deviation = 15.18

standard deviation of sample mean = 15.18/40 = 2.4

z value for 47.5 is (47.5-48)/2.4 is -0.2083, corresponding p value is 0.417497

P(X<48) = 0.5 (48 is mean)

P(47.5<X<48) = 0.5 - P(X<47.5) = 0.5-0.417497 = 0.082503 ~ 0.0832

so answer is (B)

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