According to a government study15 of all children live in a

According to a government study,15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:

a) what is the probability that 4 or more live in poverty?

b) what is the probability that 3 live in poverty?

c) what is the expected number (mean) that live in poverty?

Solution

According to a government study,15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:

Excel used

Binomial Probabilities

Data

Sample size

15

Probability of an event of interest

0.15

Statistics

Mean

2.25

Variance

1.9125

Standard deviation

1.3829

Binomial Probabilities Table

X

P(X)

0

0.0874

1

0.2312

2

0.2856

3

0.2184

4

0.1156

5

0.0449

6

0.0132

7

0.0030

8

0.0005

9

0.0001

10

0.0000

11

0.0000

12

0.0000

13

0.0000

14

0.0000

15

0.0000

P( x >=4) =0.1773

P( x =3) =0.2184

c) what is the expected number (mean) that live in poverty?

Mean =np=15*0.15=2.25

Binomial Probabilities
Data
Sample size	15
Probability of an event of interest	0.15
Statistics
Mean	2.25
Variance	1.9125
Standard deviation	1.3829
Binomial Probabilities Table
	X	P(X)
	0	0.0874
	1	0.2312
	2	0.2856
	3	0.2184
	4	0.1156
	5	0.0449
	6	0.0132
	7	0.0030
	8	0.0005
	9	0.0001
	10	0.0000
	11	0.0000
	12	0.0000
	13	0.0000
	14	0.0000
	15	0.0000