Question

A) If a seed is planted, it has a 80% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 1 doesn't grow?

B) About 8% of the population has a particular genetic mutation. 700 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 700.

Answer 1

A) This question is a case of binomial distribution. So, total number of seeds planted (n) = 8. Probability of a seed growing into healthy plant(p) = 80% = 0.8

So, q = 1-p = 1-0.8 = 0.2

So, Probability that out of 8 seeds, exactly 1 seed doesn’t grow = Probability that out of 8 seeds, exactly 7 seeds grow into healthy plant.

Let the number of seeds growing into healthy plant be X

So, P(X = 7) = ⁸C₇ * 0.8⁷ * 0.2¹

= 8 * 0.8⁷ * 0.2

= 0.3355.

So, the probability that exactly 1 seed out of 8 seeds doesn’t grow is 0.3355.

B) We have n = 700

Probability of genetic mutation (p) = 0.08

So, q = 1-p = 1-0.08 = 0.92

So, the Variance = n*p*q = 700*0.92*0.08

= 51.52.

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