Question

A frequency distribution is shown below. Complete parts (a) through (e) The number of dogs per household in a small towr Dogs Households 1427 42 5 26 11 164 41 (a) Use the frequency distribution to construct a probability distribution. P(x) Round to the nearest thousandth as needed.) (b) Find the mean of the probability distribution. (Round to the nearest tenth as needed.) (c) Find the variance of the probability distribution. ?2-O (Round to the nearest tenth as needed.) (d) Find the standard deviation of the probability distribution. ?') (Round to the nearest tenth as needed.) (e) Interpret the resuits in the context of the real-life situation. O A. A household on average has 0.5 dog with a standard deviation of 0.9 dog O B. A household on average has 0.9 dog with a standard deviation of 0.5 dog O C. A household on average has 0.8 dog with a standard deviation of 0.9 dog O D. A household on average has 0.5 dog with a standard deviation of 11 dog. Click to select your answer(s).

Answer 1

Total households = 1427 + 421 + 164 + 41 + 26 + 11 = 2090

x                  P(x)

0                 0.683

1                 0.201

2                 0.078

3                 0.020

4                 0.012

5                 0.005

b) E(X) = $\mu$ = 0 * 0.683 + 1 * 0.201 + 2 * 0.078 + 3 * 0.020 + 4 * 0.012 + 5 * 0.005 = 0.5

c) E(X^2) = 0^2 * 0.683 + 1^2 * 0.201 + 2^2 * 0.078 + 3^2 * 0.020 + 4^2 * 0.012 + 5^2 * 0.005 = 1.01

Variance( $\sigma^2$ ) = E(X^2) - (E(X))^2

               = 1.01 - (0.5)^2

               = 0.8

d) Standard deviation( $\sigma$ ) = sqrt(0.8) = 0.9

e) Option - A