Question

use the probability distribution to find probabilities in parts (a) through (c).
the probability distribution of number of dogs per household in a small town
dogs 0 1 2 3 4 5
households 0.678 0.202 0.075 0.024 0.014 0.007
(a) find the probability of randomly selecting a household that has fewer than two dogs.
0.880 (round to three decimal places as needed.)
(b) find the probability of randomly selecting a household that has at least one dog.
0.322 (round to three decimal places as needed.)
(c) find the probability of randomly selecting a household that has between one and three dogs, inclusive.
(round to three decimal places as needed.)

Explanation:

Step1: Identify the relevant probabilities

The probability of having 1 dog is \(P(1) = 0.202\), the probability of having 2 dogs is \(P(2)=0.075\), and the probability of having 3 dogs is \(P(3) = 0.024\).

Step2: Calculate the sum

We use the formula \(P(1\leq X\leq3)=P(1)+P(2)+P(3)\).
Substitute the values: \(0.202 + 0.075+0.024\).

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Answer:

\(0.301\)