Question

Suppose that Stephen is the quality control supervisor for a food distribution company. A shipment containing many thousands of apples has just arrived. Unknown to Stephen, 12% of the apples are damaged due to bruising, worms, or other defects. If Stephen samples 10 apples from the shipment, use the binomial distribution to estimate the probability that his sample will contain at least one damaged apple Give your answer as a decimal precise to at least four decimal places

Answer 1

probability that his sample will contain at least one damaged apple (P) = 0.7215

Explanation:

Given:

Probability of damaged apples (p) = 12% = 0.12

number of samples (n) = 10

Consider,

x- number of apples damaged.

Using Binomial distribution formula:

P(x) =
`(nCx) (P)^x (1-p)^(n-x)`

To find the probability that his sample will contain at least one damaged apple:

P(x≥1) = 1 - P(x<1)

= 1 - P(x=0)

= 1 -
`10C_0 (0.12)^0 ( 1-0.12)^(10)`

P(x≥1) = 0.7215