Based on data from a car bumper sticker study, when a car is randomly selected,

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. Complete parts (a) through (d). Click the icon to view the data table. No Yes b. Assuming that a probability distribution is described, find its mean and standard deviation. The mean is (Round to the nearest tenth as needed.) The standard deviation is (Round to the nearest tenth as needed.) c. Use the range rule of thumb to identify the range of values for usual numbers of bumper stickers. The maximum usual value is (Round to the nearest tenth as needed.) The minimum usual value is (Round to the nearest tenth as needed.) d. Is it unusual for a car to have more than one bumper sticker? Explain. A. Yes, because the probabilities for random variable x from 2 to 9 are al less than 0.05. B. No, because the probability of more than 1 bumper sticker is 0.123, which is greater than 0.05. C. No, because the probability of having 1 bumper sticker is 0.076, which is greater than 0.05. D. Not enough information is given.

Explanation / Answer

following information has been generated using ms-excel

(a) Yes, this is probability distribution as sum of probability is 1 i.e. sum(P(x))=1

(b) mean=E(x)=sum(x*P(x))=0.54

Stanadard deviation=sqrt(variance)=sqrt(1.993)=1.41

E(x2)=sum(x2*P(x))=2.282

variance(x)=E(x2) - (E(x))2=2.282-0.538*0.538=1.993

(c) maximum value=9 and

minimimum value=0

range=maximum-minimum=9-0=9

(d) P(x>1)=1-P(x<=1)=1-(P(x=0)+P(x=1))=1-(0.801+0.076)=0.123

right choice is A. because the probability for random variable x from 2 to 9 are all less than 0.05

x P(x) x*P(x) x2*P(x) 0 0.801 0 0 1 0.076 0.076 0.076 2 0.045 0.09 0.18 3 0.027 0.081 0.243 4 0.014 0.056 0.224 5 0.014 0.07 0.35 6 0.008 0.048 0.288 7 0.006 0.042 0.294 8 0.006 0.048 0.384 9 0.003 0.027 0.243 sum= 1.000 0.538 2.282

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