Question

4. 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 follows: 0 (0.797); 1 (0.099); 2 (0.036); 3 (0.017); 4 (0.013); 5 (0.011); 6 (0.009); 7 (0.007); 8 (0.006); 9 (0.005). a. Does the given information describe a probability distribution? Why or why not? b. Would it be unusual for a car to have more than two bumper stickers? Explain this!

Answer 1

Let x be the number of bumper stickers and P(x) be its corresponding probabilities.

Given probability distribution is

x	0	1	2	3	4	5	6	7	8	9
P(x)	0.797	0.099	0.036	0.017	0.013	0.011	0.009	0.007	0.006	0.005

Here sum of all probabilities = 1

So the given distribution is probability distribution.

Probability that car have more than two bumper stickers

= P(X = 3) + P(X= 4) + P(X = 5) + P(X = 6) + P(X = 7) +P(X = 8) + P(X = 9)

= 0.017 + 0.013 + 0.011 + 0.009 + 0.007 + 0.006 + 0.005

= 0.068

Probability that car have more than two bumper stickers is 0.068

Probability that car have more than two bumper stickers = 0.068 > 0.05.

So we can say that it is not unusual.

It would not be unusual for a car to have more than two bumper stickers.