Question

Suppose a biological cell contains 400 genes. When treated radioactively the probability that
a gene will change into mutant gene is 0.006 and is independent of the other genes. What is
the approximate probability that there are at most 4 mutant genes after the treatment?

Answer 1

Question #68578, Math / Statistics and Probability

Suppose a biological cell contains 400 genes. When treated radioactively the probability that a gene will change into mutant gene is 0.006 and is independent of the other genes. What is the approximate probability that there are at most 4 mutant genes after the treatment?

Answer.

Normal probability with $\mu = np = 0.006 * 400 = 2.4$,

$$\sigma = \sqrt{np(1 - p)} = \sqrt{400 * 0.006(1 - 0.006)} = 1.5445.$$ $$P(X \leq 4) = P\left(Z \leq \frac{4 - 2.4}{1.5445}\right) = P(Z \leq 1.04) = 0.8508.$$

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