Question
In: Statistics and Probability
A manufacturer issues a recall for a particular model of baby stroller because a small number...
A manufacturer issues a recall for a particular model of baby stroller because a small number of them have collapsed, injuring the baby. A store has 45 of these strollers returned as a result of the recall. X is the number of defective strollers out of those returned. Is X binomial? Can you please explain why it isn't?
Solutions
Expert Solution
Solution: In the given problem, X is the number of defective strollers out of all the 45 strollers returned. It is not a binomial random variable but a Poisson random variable.
The difference between these two is that, with a Binomial random variable, we can have a certain number of events, each having the probability of success "p". But with Poisson random variable, we have infinite attempts with a very small probability of success. If we have the number of attempts, n, that tends to infinity and probability of success, p, that is infinitesimally small, that is tending to zero, then, n*p --> lambda, then the distribution approaches a Poisson Distribution with parameter lambda.
Thus, Poisson Distribution is used in those situations where occurrences of events can happen for a very large number of times but rarely happens.
Here, baby stroller is manufactured in a large quantity, 45 of them have been returned, (45>30), so sample size can be considered to be large. Also, it is stated that only a small number of the lot have collapsed. So, it is suggestive that n is large and p is small and therefore, X is not a binomial random variable but a Poisson random variable.
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