For each of the following situations, tell whether or not the specific random va
ID: 3364609 • Letter: F
Question
For each of the following situations, tell whether or not the specific random variable X has a binomial distribution.
If the random variable X does have a binomial distribution, X ~B(n, p), give its description, i.e., indicate the values of n and p.
If it does not, explain why not. Which of the five characteristics of a binomial distribution are not satisfied? State at least one.
1. From past records, a salesperson determined that she makes a sale to 20% of her customers. One day, she counted the number of customers until she made a sale. Let X be the number of customers until her first sale.
(a) The distribution of X is binomial with n = ___________ and p = ____________
Explain:
2. From past records, a salesperson determined that she makes a sale to 20% of her customers. One day, 30 people entered the store from 8:30am to 9:30am. Let X be the number of customers who did make a purchase during that one-hour period.
(a) The distribution of X is binomial with n = ____________ and p = ____________ Or (b) The distribution of X is not binomial because ....
Explain:
Explanation / Answer
Solution :
For each of the following situations, tell whether or not the specific random variable X has a binomial distribution.
1. From past records, a salesperson determined that she makes a sale to 20% of her customers. One day, she counted the number of customers until she made a sale. Let X be the number of customers until her first sale.
In Binomial probability distribution n = number of trials are fixed.
Since in above situation number of customers are not fixed.
Thus this is not a Binomial probability distribution.
Part 2. From past records, a salesperson determined that she makes a sale to 20% of her customers. One day, 30 people entered the store from 8:30am to 9:30am. Let X be the number of customers who did make a purchase during that one-hour period.
In above situation : n = number of customers = 30 and p = probability of success = 0.20
and number of trials are independent
thus The distribution of X is binomial with n = 30 and p = 0.20
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