1 described the concept of a discrete probability distributi

1) described the concept of a discrete probability distribution, and then described the binomial probability distribution. Are all discrete probability distributions binomial? Why or why not?

2) Based on data from CarMax.com, when a car is randomly selected, the number of bumper stickers and that corresponding probabilities are 0 (.824); 1(.083); 2 (.039); 3(.014); 4 (.012); 5 (.008); 6 (.008); 7 (.004); 8 (.004); 9(.004).

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.

Solution

1.

Not all discrete probability distributions are binomial.

For a distribution to be binomial, then there must only be two possible results, a success and a failure. Thus, is we have 3 or more possible results, even though it is discrete, it will no longer be binomial.

Also, the probability of a success has to be constant. So, even if you only have two possible results, if the probability of success is not constant, it is not binomial. For example, getting 3 balls inside a bag with 5 black and 5 white balls, without replacement.

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