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 0.665 0.209 0.084 0.022 0.014 0.006

(a) find the mean, variance, and standard deviation of the probability distribution.
find the mean of the probability distribution.
μ = 0.5 (round to one decimal place as needed.)
find the variance of the probability distribution.
σ² = 0.8 (round to one decimal place as needed.)
find the standard deviation of the probability distribution.
σ = (round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation \(\sigma\) of a probability distribution is the square root of the variance \(\sigma^2\), i.e., \(\sigma=\sqrt{\sigma^2}\).

Step2: Substitute the given variance

We are given that \(\sigma^2 = 0.8\). So we calculate \(\sigma=\sqrt{0.8}\).

Step3: Compute and round

\(\sqrt{0.8}\approx0.9\) (rounded to one decimal place).

Answer:

\(0.9\)