Question

An agency collects demographics concerning the number of people in families per household in a certain country. Assume the distribution of the number of people per household is as shown in the table to the right. a. Calculate the expected number of people in families per household in the country. b. Compute the standard deviation of the number of people in families per household.

x ​P(x)    2 0.25 3 0.24 4 0.31 5 0.12 6 0.05 7 0.03

a. The expected number of people in families per household is

​(Type an integer or a​ decimal.)

b. The standard deviation of the number of people in families per household is

​(Type an integer or decimal rounded to four decimal places as​ needed.)

2.- A survey reported that 39​% of people plan to spend more on eating out after they retire. If ten people are randomly​ selected, determine the values below.

a.	The expected number of people who plan to spend more on eating out after they retire
b.	The standard deviation of the individuals who plan to spend more on eating out after they retire
c.	The probability that two or fewer in the sample indicate that they actually plan to spend more on eating out after retirement

a. The expected number of people who plan to spend more on eating out after they retire is :? people. ​(Type an integer or a​ decimal.)

b. The standard deviation of the individuals who plan to spend more on eating out after they retire is : people.

​(Round to four decimal places as​ needed.)

c. The probability that two or fewer people in the sample indicate that they actually plan to spend more on eating out after retirement is

​(Round to four decimal places as​ needed.)

Answer 1

Solution : Part-1: house hold. Given that x denotes number of people in families per given follows: and its distribution is as xw Pa) 0.25 0.24 4 0.31 UT 0-12 6 0.05 7 0.03 household (a) Expeeted number of people in families per E(X) 2. 2 P(x=2) 7 ZEZ = 2 P(x-2) + 3 P(X=3) + 4 F(X= 4)+5.P(X=5) + 6 P(X+6) + 7 P(x = 1) (2x0•25) + (3X0-24) + (4X0-31) +(5X0-12)+(6x0º05) (FX0-03) 3.57. in families per household (6) Variance of number of people Var(x) = E(X3) -(E(x))? z? P(X=2) - (3:57)? 7 2=2 = (4 *0-25)+(9x0.24) +(16X0-31) +(25*0.12) + (36 *0.05) + (49x0-03) - (3:57) 1.6451 -> standard deviation Var (8) J1-6451 1.2826 (Ans.)