Question

We are doing a study on shampoo buyers in Walmart stores across the US and we send them online surveys. Based on past studies, we know that of the people who start the survey, 80% qualify for the study, and only 40% of these people who do qualify actually complete the survey. Of the people who complete the survey, 10% of respondents are removed due to invalid or low quality answers. If we want 1000 valid responses for this particular study, how many people do we need to have start the survey?

Answer 1

Number of people = 3473

Explanation:

Probability is typically the rate at which an event or occurrence is likely to happen. Whenever we're not so sure about an event outcome, we can then deliberate about the probabilities or possibility of certain outcomes that is how likely they are to happen.

Probability of success, =0.8×0.4×0.9 =0.288

Expected, E=1000

Expected = np

1000=n×0.288

n=​0.288​​1000​​≈34

Answer 2

2500

Explanation:

They tell you that only 40% of the total complete the quality test, and you want to know how many represent 100%.

If this 40% is 1000 valid responses use cross multiplication to know how many people are the total.

40%-----1000 valid responses

100%----x=

`(100*1000)/(40) =X\\2500=X`

So, you can tell they need at least 2500 persons to have 1000 valid responses.