Question

a surfboard factory just discovered a manufacturing error that causes some of the surfboards to crack easily. as a result, the factory recalled all of the surfboards sold in the last year. each surfboard has a 20% chance of having the defect. if the factory recalled 2 surfboards, what is the variance of the number of surfboards with the defect? write your answer as a decimal.

Explanation:

Step1: Identify the distribution

This is a binomial distribution problem. The binomial distribution formula for variance is \(Var(X)=np(1 - p)\), where \(n\) is the number of trials and \(p\) is the probability of success.

Step2: Substitute the values

Here, \(n = 2\) (number of surfboards recalled) and \(p=0.2\) (probability of a surfboard having the defect). Then \(1-p = 1 - 0.2=0.8\).
Substitute into the formula: \(Var(X)=2\times0.2\times0.8\).

Step3: Calculate the result

\(2\times0.2\times0.8 = 0.32\)

Answer:

\(0.32\)