Question

The chance that any jug of milk in the grocery store will be sour is 5%. Suppose you purchase 20 jugs of milk for the summer camp where you work. What is the expected number of jugs of sour milk in your purchase

Answer 1

Given that

Chance that any jug of milk in grocery store will sour is 5%

i.e

p : Probability that a randomly selected jug of milk in grocery store will sour = 5/100 = 0.05

n : Number of jugs of milk purchased for the summer camp where you work = 20

X : Number of jugs of sour milk in your purchase

X follows a Binomial distribution with n=20 and p = 0.05

Expected value of Binomial distribution : E(X) = np

Therefore,

Expected number of jugs of sour milk in your purchase = E(X) = np = 20 x 0.05 =1

Expected number of jugs of sour milk in your purchase = 1

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The chance that any jug of milk in the grocery store will be sour is 5%

i.e if 100 jugs of milk are purchased from a grocery store then there is chance of 5 jugs of milk being sour

therefore, if 20 jugs of milk are purchased then (20x5)/100 = 1 jug of milk is expected to be sour.

Expected number of jugs of sour milk in a purchase of 20 jugs of milk = 1