Question

A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be 28%. We are interested in the number of dealerships she must call.

1. In words, define the random variable X.
2. List the values that X may take on.
3. Give the distribution of X. X ~ _____(_____,_____)
4. On average, how many dealerships would we expect her to have to call until she finds one that has the car?
5. Find the probability that she must call at most four dealerships.
6. Find the probability that she must call three or four dealerships.

Answer 1

Solution:

a) The given random variable X can be defined as

X : The number of dealerships Miata must call

b) For the Given data , The above random variables X will take following values

x = 0,1,2..

c)Given that dealerships of 28% have the car

Therefore the data will be geometric distribution

X ~ G(0.28)

d) The average for geometric distribution

μ = 1 /p = 1 /0.28 = 3.57

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