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 = 0.9 (round to one decimal place as needed.) (b) interpret the results in the context of the real - life situation. a. a household on average has 0.5 dog with a standard deviation of 0.9 dog. b. a household on average has 0.8 dog with a standard deviation of 0.9 dog. c. a household on average has 0.5 dog with a standard deviation of 11 dogs. d. a household on average has 0.9 dog with a standard deviation of 0.5 dog.

Explanation:

Step1: Recall Mean and Std Dev

From part (a), mean ($\mu$) is 0.5, standard deviation ($\sigma$) is 0.9.

Step2: Evaluate Options

• Option A: Matches mean (0.5) and std dev (0.9).
• Option B: Mean is wrong (0.8 is variance).
• Option C: Std dev (11) is wrong.
• Option D: Both mean and std dev are wrong.

Answer:

A. A household on average has 0.5 dog with a standard deviation of 0.9 dog.