Question

1. A study conducted by a TV station showed the number of televisions per household and the corresponding probabilities for each. Find the mean, variance, and standard deviation.

x (Number of TV’s)	P(x)	xP(x)	x2	x2P(x)
1	0.32
2	0.51
3	0.12
4	0.05

1. Find the probability a household owns more than 2 televisions?             (1 pt.)
2. Find the probability a household owns at most 2 televisions?                 (1 pt.)
3. Find the mean, variance, and standard deviation. (Fill in the table)        (8 pts.)
4. If you were taking a survey on the programs that were watched on television, how many program diaries would you send to each household in the survey?            (1 pt.)
5. A household claims that they own 7 televisions. Do you think that this is a believable claim? Explain.                                                                                                    (3 pts.)

Answer 1

x	P(x)	xP(x)	x2	x2P(x)
1	0.32	0.32	1	0.32
2	0.51	1.02	4	2.04
3	0.12	0.36	9	1.08
4	0.05	0.20	16	0.80
		1.90		4.24

(a) Probability that a household owns more than 2 televisions = P(X > 2) = 0.12 + 0.05 = 0.17

(b) Probability that a household owns at most 2 telivisions = P(X ≤ 2) = 0.83

(c) Mean = $\sum xP(x)$ = 1.90

Variance = $\sum x^{2}P(x) - \mu^{2}$ = 0.63

Standard deviation = √0.63 = 0.794

(d) Since the mean in 1.90, we would send 2 program diaries to each household in the survey

(e) No, this is not a believable claim since it is even high than the maximum number of televisions in a household which is 4