Mathematics, 20.06.2020 03:57 jj11vb

The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9.8% 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.(b) Assuming his suspicion that 9.8% 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?

Answers: 2

Show answers

Answers

Answer from: ijeomaokoro9488

Using the binomial distribution, it is found that:

b) There is a 0.2088 = 20.88% probability that exactly 2 out of the first 11 customers buy a magazine.

c) The expected number of customers from this sample that will buy a magazine is of 1.078.

For each customer, there are only two possible outcomes, either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of any other customer, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.

In this problem:

9.8% of his customers buy a magazine, hence p = 0.098

A sample of 11 customers is taken, hence n = 11

Item b:

The probability is P(X = 2), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{11,2}.(0.098)^{2}.(0.902)^{9} = 0.2088$

There is a 0.2088 = 20.88% probability that exactly 2 out of the first 11 customers buy a magazine.

Item c:

The expected value of the binomial distribution is given by:

E(X) = np

Hence:

E(X) = 11(0.098) = 1.078

The expected number of customers from this sample that will buy a magazine is of 1.078.

To learn more about the binomial distribution, you can check link

Answer from: leo4687

Step-by-step explanation:

Let x be a random variable representing the number of his customers that buy a magazine. This is a binomial distribution since the outcomes are two ways. It is either a selected customer buys a magazine or he doesn't. The probability of success, p = 9.8/100 = 0.098

The probability of failure, q would be 1 - p = 1 - 0.098 = 0.902

b We want to determine P(x = 2)

n = 11

From the binomial distribution calculator,

P(x = 2) = 0.21

c) the expected number of customers from this sample that will buy a magazine is same as the mean.

mean = np

mean = 11 × 0.098 = 1.08

Answer from: Quest

the answer to this question is 3/19

step-by-step explanation:

Answer from: Quest

Socrat use det app ok

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:00, sanafarghal

Simplify. (-2)^-3 a. -8 b. -1/8 c. 1/8 d. 8

Answers: 1

continue

Mathematics, 21.06.2019 19:30, cody6187

Agroup of randomly selected apple valley high school students were asked to pick their favorite gym class. the table below shows the results of the survey. there are 528 students at apple valley high school. gym class number of students racquet sports 1 team sports 9 track and field 17 bowling 13 based on the data, what is the most reasonable estimate for the number of students at apple valley high school whose favorite gym class is bowling? choose 1 answer a. 9 b. 13 c. 119 d. 172

Answers: 1

continue

Mathematics, 21.06.2019 21:00, batmanmarie2004

The functions below show the amount of money bella and sweet t had saved after earning money for doing chores. which description best compares the two functions?

Answers: 1

continue

Mathematics, 22.06.2019 01:50, iiMxlissaii

Grandpa ernie is shrinking! over the past 4 years his height decreased by a total of 2.4 cm. it decreased by the same amount each year. what was the change in grandpa ernie's height each year

Answers: 2

continue

You know the right answer?

The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects...