Question

Sixty percent of the customers who go to Sears Auto Center for tires buy four tires and 22% buy two tires. Moreover, 14% buy fewer than two tires, with 4% buying none. a. What is the probability that a customer buys three tires? (Round your answer to 2 decimal places.) b. Construct a cumulative probability distribution for the number of tires bought. (Round your answer to 2 decimal places.)

Answer 1

Given that, 60% buy 4 tires, 22% buy 2 tires, 14% buy fewer than 2 tires and 4% buy zero tire.

Herw, 14% buy fewer than 2, mean 14% buy 1 and zero tiers

So, 14 - 4 = 10% buy 1 tire

Let X be a number of tires

and P(x) be the probability of buying tires.

Here, x = 0 has P(x) = 4% = 0.04

x = 1 has P(x) = 0.10, x = 2 has P(x) = 0.22 and

x = 4 has P(x) = 0.60

We know, total probability is 1

so, P(x= 3) = 1 - [ 0.04 + 0.10 + 0.22 + 0.60] = 1 - 0.96 = 0.04

Therefore, the probability that a customer buys three tires is 0.04

b) Cumulative probability distribution for the number of tires bought is as follows,

X	P(X <= x)
0	0.04
1	0.14
2	0.36
3	0.40
4	1.00