Question

We are interested in the number of times a teenager must be reminded to do his or her chores each week. A survey of 40 mothers was conducted. Table B16 shows the results of the survey. IX P(x) 0 40 1 40 N 3 14 40 4 40 5 Table B16 Find the expected number of times a teenager is reminded to do his or her chores. Select one: a. 2.78 b. 1.0 C. 15 d. 3.13

Answer 1

We find the missing value of P (x) for x = 2

Consider P(x) for x = 2 is k

Sum of all probabilities is always 1

$\sum P(x) = 1$

2 14 4 + + - + +E+ 40 1 40 40 40 40

c+ 2+5+14+7+4 40 - 1

32 k+ 40

k=1- 32 40

$k = \frac{40- 32}{40}$

$k = \frac{8}{40}$

P(X) for x = 2 is

$\frac{8}{40}$

The formula of expected value

$Expected \ value = \sum x*P(x)$

x	P(X)	x*P(x)
0	$\frac{2}{40}$	$0*\frac{2}{40}= {\color{Purple} 0}$
1	$\frac{5}{40}$	5 5 1 * 40 40
2	$\frac{8}{40}$	$2*\frac{8}{40}= {\color{Purple}\frac{16}{40} }$
3	$\frac{14}{40}$	$3*\frac{14}{40}= {\color{Purple}\frac{42}{40} }$
4	$\frac{7}{40}$	$4*\frac{7}{40}= {\color{Purple}\frac{28}{40} }$
5	$\frac{4}{40}$	$5*\frac{4}{40}= {\color{Purple}\frac{20}{40} }$

$expected \ value = \sum x*P(x) = 0+ \frac{5}{40}+ \frac{16}{40}+ \frac{42}{40}+ \frac{28}{40}+ \frac{20}{40}$

$expected \ value = \sum x*P(x) = \frac{0+5+16+42+28+20}{40}$

$expected \ value = \sum x*P(x) = \frac{111}{40} = 2.775$

Round the expected value up to 2 decimal

$expected \ value = \sum x*P(x) ={\color{Purple} 2.78}$

Final answer:-

The correct choice is (a)

Expected number of times a teenager is reminded to do his or her chores = 2.78