One day Karen bought 24 random cans of soup from a grocery store. Suppose that 7

Question

One day Karen bought 24 random cans of soup from a grocery store. Suppose that 7% of can sold at that particular grocery store are dented and assume the store’s inventory is large enough that no individual customer’s purchase affects the dent rate for the remaining cans. One day Karen bought 24 random cans of soup from a grocery store. Suppose that 7% of can sold at that particular grocery store are dented and assume the store’s inventory is large enough that no individual customer’s purchase affects the dent rate for the remaining cans.

Explanation / Answer

In this problem, we have to model this as a Binomial distribution with the following parameters:

n = 24, p = 0.07

Let X denote the RV for the number of cans that are dented.

So,

P(X=x) = nCx*(px)*(1-p)n-x

Putting values we get:

P(X=x) = 24Cx*(0.07x)*(1-0.07)24-x

So, suppose we want to find the probability that only 4 cans out of the 24 purchased are dented. So,

P(X=4) = 24C4*(0.074)*(1-0.07)24-4

Solving we get:

P(X=4) = 0.0597

Hope this helps !

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