Question

Construct a probability distribution, graph the probability distribution using a histogram and describe its shape.

•  Cars The number of Sedan cars per household in a small town

Cars 0 1 2 3

Households 598 462 381 259

• Use the probability distribution you made in the exercise below to find the probability of randomly selecting a household that has (a) one or two cars, (b) less than two cars, (c) between one and three cars, inclusive, and (d) at least two cars.
• In the exercise, would it be unusual for a household to have three Sedan cars? Explain your reasoning.

Answer 1

We calculated $P(X=x)=\frac{n(x)}{\sum{n(x)}}=\frac{n(x)}{1700}$

Histogram is linearly decreasing.

$a:\\P\left( X=1 \right) +P\left( X=2 \right) =0.271765+0.224118=0.495883\\b:\\P\left( X=0 \right) +P\left( X=1 \right) =0.351765+0.271765=0.62353\\c:\\1-P\left( X=0 \right) =1-0.351765=0.648235\\d:\\P\left( X=2 \right) +P\left( X=3 \right) =0.224118+0.152353=0.376471$

It is unusual to have 3 cars since the probability of this event is rather small.