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# Binomial Probability Distributions - Sample Surveys

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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?

https://brainmass.com/math/probability/binomial-probability-distributions-sample-surveys-575671

#### Solution Preview

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.

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## This problem shows how to calculate probabilities and percentiles from normal and binomial probability distributions.

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A company that sells annuitites must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and and a standard deviation of 3.5 years. What proportion of the plan recipients would recieve payments beyond age 75?

A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of american hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability of all the hotels in the sample that offer hairdryers in the bathrooms.

A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of american hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that at least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled between 16 and 21 minutes.

A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
0.0256
0.0625
0.16
1.00

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