Question
Asked Dec 2, 2019
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A manufacturer ships toaster s in cartons of 20 In each carton , they estimate a 5% chance that one of the toasters will need to be sent back for minor repairs. What is the probability that in a carton , there will be exactly 5 toasters that need repair?

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Expert Answer

Step 1

Solution:

Binomial distribution:

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable X is given as:

п
x 0,1,0p <l;q 1- p
X
n-x
P(X=x)
2
х
1
otherwise
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п x 0,1,0p <l;q 1- p X n-x P(X=x) 2 х 1 otherwise

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Step 2

The probability that in a carton, there will be exactly 5 toasters that need repair is obtained below:

From the given information, number of ships toaster s in cartons of 20 in each cart...

Using the EXCEL formula,
P(X 5) 0.0022
=BINOM.DIST (5,20,0.05,FALSE)
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Using the EXCEL formula, P(X 5) 0.0022 =BINOM.DIST (5,20,0.05,FALSE)

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