Question

complete parts (a) and (b) below
the number of dogs per household in a small town
dogs 0 1 2 3 4 5
probability 0.655 0.214 0.084 0.023 0.015 0.009
(a) find the mean, variance, and standard deviation of the probability distribution.
find the mean of the probability distribution.
μ = □ (round to one decimal place as needed )

Explanation:

Step1: Recall the formula for the mean of a probability distribution

The formula for the mean \(\mu=\sum_{x}x\cdot P(x)\), where \(x\) is the value of the random variable and \(P(x)\) is the corresponding probability.

Step2: Calculate each term \(x\cdot P(x)\)

• For \(x = 0\): \(0\times0.655=0\)
• For \(x = 1\): \(1\times0.214 = 0.214\)
• For \(x = 2\): \(2\times0.084=0.168\)
• For \(x = 3\): \(3\times0.023 = 0.069\)
• For \(x = 4\): \(4\times0.015=0.06\)
• For \(x = 5\): \(5\times0.009 = 0.045\)

Step3: Sum up the terms

\(\mu=0 + 0.214+0.168 + 0.069+0.06+0.045\)
\(\mu=0.556\)

Answer:

\(0.6\)