Binomial Probability Distributions - Sample Surveys

Binomial probability distributions are used in business, science, engineering, and other fields. Suppose you work for a marketing agency and have to create a television ad for Brand A toothpaste. The toothpaste manufacturer claims that 40% of the toothpaste buyers prefer Brand A to Brand B. Your agency conducts a survey to check whether this claim is reasonable.

Respond to the following:

1.How would you do the sample survey?
- Explain how you would conduct the survey.
- What are the ethical implications if the manufacturer of Brand A toothpaste asked you to survey only its employees?

2.How would you interpret the outcomes?
- After conducting a random sample of people who do not work for the manufacturer, you found that 35/100 prefer Brand A. Could the manufacturer's claim still be true?
- Your random sample of 100 found only 25 people who preferred Brand A. Would you still be justified in running the ad?

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Binomial probability distributions

Binomial probability distributions are used in business, science, engineering, and other fields. Suppose you work for a marketing agency and have to create a television ad for Brand A toothpaste. The toothpaste manufacturer claims that 40% of the toothpaste buyers prefer Brand A to Brand B. Your agency conducts a survey to check whether this claim is reasonable.

Respond to the following:

1. How would you do the sample survey?
Explain how you would conduct the survey.

We are required to ...

Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375?

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Nathan wants to approximate a binomialprobability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95.
Can Nathan use the normal curve area to approximate a binomialprobability?

Nathan wants to approximate a binomialprobability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95
Can Nathan use the normal curve area to approximate a binomialprobability?

Please see the attached file for the fully formatted problems.
1. Explain the difference between a discrete and a continuous random variable. Give two examples of each type of random variable.
2. Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
a

Answer the following:
(A) Find the binomialprobability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomialprobability P(x is at most 6) using probability notation.

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