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A tire company produced a batch of 5 comma 300 tires that includes exactly 260 that...

A tire company produced a batch of 5 comma 300 tires that includes exactly 260 that are defective. a. If 4 tires are randomly selected for installation on a​ car, what is the probability that they are all​ good? b. If 100 tires are randomly selected for shipment to an​ outlet, what is the probability that they are all​ good? Should this outlet plan to deal with defective tires returned by​ consumers?

Solutions

Expert Solution

From the information, the number of tires in the experiment be . The tires for installation on a car are assumed to be independent of each other.

The possible outcomes are the tires are “defective” and “good”. Let X be the number of tires are defective. Here, the requirements of a binomial experiment are satisfied. Hence, the binomial distribution is appropriate.

From the given information, and .

The probability that they are all good when 4 tires are randomly selected for installation on a car is obtained as given below:

P(all are good) = P(no defective)
= P(X=0)
=

The probability that all the tires are good is 0.818.


From the information, the sample size is 100 tires with probability of 0.0426. The probability that tires are all good is obtained by substituting corresponding values in the .

From the given information, and .

The probability that tires are all good when 100 tires are randomly selected for shipment to an outlet is obtained as given below:
P(all are good) = P(no defective)
= P(X=0)

=

The probability that tires are all good when 100 tires are randomly selected for shipment to an outlet is 0.0066.


The probability that all the tires are good is 0.8402.
The probability that tires are all good when 100 tires are randomly selected for shipment to an outlet is 0.0066.

Yes, because there is a very small possibility that all 100 tires are good.

milcah answered 11 months ago
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