Question

You are randomly approaching people to take part in a survey. You originally assume that the probability that a randomly approached person agrees to take your survey is 4%. Of the first 10 people you approach, 5 agree to take your survey.

What can you infer about your original assumption?

		Even though 5 of the first 10 people agreed to take the survey, the sample is too small to draw any conclusions about your original assumption.
		The original assumption will require a higher margin of error to compensate for the high proportion of people that initially agreed to take the survey.
		If the original assumption that only 4% of people will take the survey were correct, then it is an extremely rare event for 5 of the first 10 people to take it, so you should doubt/reject the original assumption.
		Even though a high portion of people initially agreed to the survey, the Law of Large Numbers states that as you survey more and more people the number that agree to take it will approach 4%

Answer 1

We are given here that:
P(agreed to survey) = p = 0.04

The probability that 5 or more agree to take the survey is computed here as:

P(X >= 5) = 1 - P(X <= 4)

This is computed using the binomial probability function in EXCEL as:
=1-binom.dist(4,10,0.04,TRUE)

The output here is 0.000022

As the probability here is 0.000022 < < 0.05, therefore the given event is extremely rare given that the given probability is true. Therefore c is the correct answer here.