Question

Use the normal distribution to approximate the binomial probability that more than 90 of 100 scorpion stings will cause extreme discomfort if the probability is 0.82 that any one of them will cause extreme discomfort.

Answer 1

This is a binomial distribution question with

n = 100

p = 0.82

q = 1 - p = 0.18

This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5

Since we know that

P(x > 90.0)=?

The z-score at x = 90.0 is,

z = 2.0823

This implies that

P(x > 90.0) = P(z > 2.0823) = 1 - P(z < 2.0823) = 1 - 0.9813424620403914

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