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A major automobile manufacturing company is known to average five defects per car.

Consider the next car made. Find the probability that it has exactly seven defects.

Answer :

Final answer:

Using the Poisson probability distribution, we can calculate that there is approximately a 10.4% probability that the next car produced by the company will have exactly seven defects.

Explanation:

This question is about the concept of a Poisson probability distribution. A Poisson distribution models the number of events (in this case, defects) that occur in a fixed interval of time or space (in this case, one car) with a known average rate (in this case, five defects per car).

In this case, we want to find the probability that the next car has exactly seven defects. The formula for the Poisson probability is: P(x; μ) = (e^-μ) * (μ^x) / x!, where 'e' is the base of the natural logarithm (approximately 2.71828), 'μ' is the average rate (5 defects), 'x' is the actual number of successes that result from the experiment (7 defects), and 'x!' means 'x factorial'.

So, in the case of the car manufacturing company, we substitute these values into the formula: P(7; 5) = (e^-5) * (5^7) / 7! = approximately 0.104. Hence, there is approximately a 10.4% probability that the next car will have exactly seven defects.

Learn more about Poisson Probability here:

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