Question

Show Intro/Instruction To earn full credit for this question, use your own sheet of paper to solve the problem, showing all steps of your work in order to get full credit. The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9% 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. (b) Assuming his suspicion that 9% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 10 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? Use the space below to type your answer AND/OR to upload a picture of your work for all the questions in this problem. To upload a picture of your work, use a cellphone camera or o free scanning app such as Adobe Scan, Simple Scanner, Tiny Scan download the picture or document to your own computer via email and attach your document using the attach le sign on the menu bor below.

Answer 1

Question (a)

It is a binomial experiment because

1) Customers buying magazines take decisions independent of each other because a customer buying magazine does not effect the decision of another cstomer buying a magazine

So the trials are independent

2) There are only two outcomes here. Customer buying a magazine or not buying a magazine

So there are only two outcomes

3) The probability of each customer buying a magazine is 0.09 and it remains the same for all the customers

4) There will be a finite number of customers so the number of trials are fixed

Question (b)

We need to find the probability that exactly 5 out of the first 10 customers buy a magazine

Given that the probability a customer buys a magazine = 9% or 0.09

The number of successes x in n trails in binomial distribution = * px * (1-p)n-x

72 2

= n! / [ x! (n-x)! ] * px * (1-p)n-x

Here p = 0.09, n = 10, x = 5

So probability that exactly 5 out of the first 10 customers buy a magazine = $\binom{10}{5}$ * 0.095 * (1 - 0.09)10-5

= 10! / [ 5! (10-5)! ] * 0.0000059 * (0.91)5

= 252 * 0.0000059 * 0.624032

= 0.000928528

= 0.00 rounded to two decimal digits

So probability that exactly 5 out of the first 10 customers buy a magazine = 0.00 rounded to two decimal places

The probability without rounding is 0.000928528

Question (c)

The expected number of customer from this sample that will buy the magazine

Expected value or Mean of a binomial distribution = n * p

Here n = 10 , p = 0.09

The expected number of customer from this sample that will buy the magazine = 10 * 0.09

= 0.9

So The expected number of customer from this sample that will buy the magazine = 0.9