PLEASE HELP ME WITH THIS QUESTION

Question

It is known that 23% of people ride public transport without paying for it. We talk to 81 people who have been on public transport in the last month. What is the probability that the sample proportion is more than 16%?

Answer 1

So to solve this we're going to want to look at the binomial probability distribution. Binomial probabilities are the tool we want when we're talking about a situation with (a) a population and a sample from that population or a number of trials (b) a yes/no property, like paying to ride or not paying, or being red or not-red (c) a probability of having that property in a single trial/sample.

The formula to use is:

_nC_x * P^x * (1–P)^n–x

And for us, n is the number of people, x is the number in our sample, and P^x is the probability that they don't pay, which is given as 0.23.

But the number we really want is the CUMULATIVE probability distribution that P(X > x). To find this we plug in the probability of not paying (0.23), the sample size (81), and the number of successes if the sample proportion IS 16% (it's 12.96, so I used 13). Then we can figure out the probability that our sample has a proportion greater than that.

You might also find this helpful ;) — https://stattrek.com/online-calculator/binomial.aspx

Hope that helps!