Question

Based on data from a car bumper sticker​ study, when a car is randomly​ selected, the number of bumper stickers and the corresponding probabilities are as shown below.

x   P(x)
0   0.800
1   0.088
2   0.045
3   0.017
4   0.014
5   0.012
6   0.009
7   0.007
8   0.006
9   0.002

A. Does the given information describe a probability​ distribution?

B. Assuming that a probability distribution is​ described, find its mean and standard deviation.

C. Use the range rule of thumb to identify the range of values for usual numbers of bumper stickers.

D. Is it unusual for a car to have more than one bumper​ sticker? Explain.

a. No, because the probability of more than 1 bumper sticker is 0.119, which is greater than 0.5.

b. Yes, because the probabilities for random variables x from 2 to 9 are all less than 0.05.

c. No, because the probability of having 1 bumper sticker is 0.099, which is greater than 0.05.

d. Not enough information is given.

Answer 1

a)Yes as sum of all probability is equal to 1 and individual probability is between 0 and 1

b)

x	f(x)	xP(x)	x2P(x)
0	0.800	0.000	0.000
1	0.088	0.088	0.088
2	0.045	0.090	0.180
3	0.017	0.051	0.153
4	0.014	0.056	0.224
5	0.012	0.060	0.300
6	0.009	0.054	0.324
7	0.007	0.049	0.343
7	0.006	0.042	0.294
9	0.002	0.018	0.162
	total	0.508	2.068
	E(x) =μ=	ΣxP(x) =	0.5080
	E(x2) =	Σx2P(x) =	2.0680
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.8099
	std deviation=	σ= √σ2 =	1.3453

from above mean =0.508

and std deviation =1.3453

c)

minimum usual value =μ-2*σ =			-2.183
maximum usual value =μ+2*σ =			3.199