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Choose an American household at random, and let the random variable X be the number of cars, including SUVs and light trucks, the residents own. The table gives the the probability model if we ignore the few households that own more than 8 cars.Number of cars X 0 1 2 3 4 5 6 7 8Probability 0.087 0.323 0.363 0.144 0.053 0.019 0.007 0.002 0.001A housing company builds houses with two?car garages. What percent of households have more cars than the garage can hold?A- 22.7%B- 41.0%C- 59.0%D- 14.4%

Respuesta :

Answer:

Option A.

Step-by-step explanation:

The given probability table is

Number of cars X: 0       1         2        3        4        5      6      7      8

Probability :0.087 0.323 0.363 0.144 0.053 0.019 0.007 0.002 0.001

It is given that a housing company builds houses with two car garages.

We need to find the percent of households have more cars than the garage can hold.

[tex]P(X>2)=1-P(X\leq 2)[/tex]

[tex]P(X>2)=1-[P(X=0)+P(X=1)+P(X=2)][/tex]

Substitute the probability values from the given table.

[tex]P(X>2)=1-[0.087+0.323+0.363][/tex]

[tex]P(X>2)=1-0.773[/tex]

[tex]P(X>2)=0.227[/tex]

It means 22.7% of households have more cars than the garage can hold.

Therefore, the correct option is A.

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