A gargon has probability 7/10 of catching any human being it sees. Using the nor

Question

A gargon has probability 7/10 of catching any human being it sees. Using the normal distribution, approximate the probability that if the Gargon sees 126 humans, it will catch at least 90 of them but no more than 100. A gargon has probability 7/10 of catching any human being it sees. Using the normal distribution, approximate the probability that if the Gargon sees 126 humans, it will catch at least 90 of them but no more than 100. A gargon has probability 7/10 of catching any human being it sees. Using the normal distribution, approximate the probability that if the Gargon sees 126 humans, it will catch at least 90 of them but no more than 100.

Explanation / Answer

n = 126, p = 0.7

Mean = n*p = 88.2
SD = sqrt(n*p*(1-p)) = 5.143928

P(90 <= X <= 100) = P(X <= 100) - P(X <= 90) = P(X < 100.5) - P(X < 90.5)
= P(Z < (100.5-88.2)/5.143928) - P(Z < (90.5-88.2)/5.143928) = P(Z<2.39) - P(Z<0.45)=0.9916-0.6736=0.318

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