Answer to Question #342783 in Statistics and Probability for Ahmad

Question #342783

In a restaurant an average of two out of every five customers asks for water with their meal. A family

of ten members arrives in the restaurant. What is the probability that:

a. Exactly seven members ask for water?

b. Less than nine members ask for water?


1
Expert's answer
2022-05-20T03:45:38-0400

Here we have a binomial distribution:

"P(x)=\\frac {n!} {(n-x)!x!}p^xq^{n-x}"

where "n=10, p=2\/5,q=1-p=3\/5"

So,

a. "P(7)=\\frac {10!} {(10-7)!7!}(\\frac 2 5)^7(\\frac 3 5 )^{10-7}=0.197*0.216=0.0425=4.25\\%"

b. "P(<9)=1-P(=9)-P(=10)"

"=1-\\frac {10!} {(10-9)!9!}(\\frac 2 5)^9(\\frac 3 5 )^{10-9}-(\\frac 2 5)^{10}=1-0.00157-0.0001=0.9983=99.83\\%"


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