Question
Asked Oct 16, 2019

A researcher is interested in conducting a mail survey. He finds out that there is a 40% response rate to such surveys. If a survey is mailed to 5 people, what is the probability that all respond?

 

-Binomial Distribution

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Step 1

The probability that all respond is obtained below:

Here, the response rate is considered as a success, 40%, that is p = 0.40. The not responses is considered as a failure, 60% (100% – 60%) of that is q = 0.60.

Therefore, the distribution is binomial distribution with sample size 5 and probability of success 0.40. That is, X~ Binomial (5, 0.40).

The formula for the probability of binomial distribution is

P(X x) p) (1-p)^here x=0,1,2,...,n for 0s ps1
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P(X x) p) (1-p)^here x=0,1,2,...,n for 0s ps1

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Step 2

The required proba...

P(X-) (0.40) (1-0.40)
(1)(0.01024)(
=0.01024
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P(X-) (0.40) (1-0.40) (1)(0.01024)( =0.01024

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