Of all customers purchasing automatic garage door openers, only one out of every

Question

Of all customers purchasing automatic garage door openers, only one out of every 140 purchase an imported Swedish model. It is very costly for the company to stock these and they want to determine whether to keep the Swedish model on their shelves. A sample of n = 420 customers purchasing automatic garage door openers are asked about their purchase. Let X = number of customers in the sample who purchase the Swedish model.

(a) Identify the distribution of X along with its parameters.

(b) Identify a distribution that can be used to approximate the true distribution of X. Verify conditions for the approximation to be valid.

(c) Regardless of your conclusion in (b), use the approximation to calculate the probability that more than 2 customers by the Swedish model.

Explanation / Answer

a) X is binomial with n = 420 and p = 1/140

b) cannot be approximated to normal since np = 3 <5

c) P(x>2) = 0.5736

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