The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 7.6% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. (a) Explain why this is a binomial experiment. trails are independent. (b) Assuming his suspicion that 7.6% of his customers buy a magazine is correct, what is the probability that exactly 2 out of the first 11 customers buy a magazine? Give your answer as a decimal number rounded to two digits. (c) What is the expected number of customers from this sample that will buy a magazine?
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 7.6% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. (a) Explain why this is a binomial experiment. trails are independent. (b) Assuming his suspicion that 7.6% of his customers buy a magazine is correct, what is the probability that exactly 2 out of the first 11 customers buy a magazine? Give your answer as a decimal number rounded to two digits. (c) What is the expected number of customers from this sample that will buy a magazine?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Understanding Binomial Experiments: An Example
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 7.6% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine.
#### (a) Explain why this is a binomial experiment.
**Answer:**
Trials are independent.
#### (b) Assuming his suspicion that 7.6% of his customers buy a magazine is correct, what is the probability that exactly 2 out of the first 11 customers buy a magazine? Give your answer as a decimal number rounded to two digits.
**Answer:**
#### (c) What is the expected number of customers from this sample that will buy a magazine?
**Answer:**
This example helps to illustrate the following key concepts in binomial experiments:
1. **Independent Trials:** Each customer's decision to buy or not buy a magazine is independent of the others.
2. **Fixed Number of Trials:** The experiment is conducted over a fixed number of trials – in this case, 11 customers.
3. **Two Possible Outcomes:** Each trial (customer interaction) results in one of two outcomes: buying a magazine or not.
4. **Constant Probability:** The probability of success (buying a magazine) remains the same for each trial, 7.6%.
These principles are crucial for understanding and solving problems involving binomial experiments.
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