In a survey, 162 respondents say that they never use a credit card, 1217 say that they use it sometimes, and 2836 say that they use it frequently. What is the probability that a randomly selected person uses a credit card frequently? Is it unlikely for someone to use a credit card frequently? How are all of these results affected by the fact that the responses were obtained by those who decided to respond to a survey posted on the Internet?

For this case this probability represent more than 50% of the participants, so we can't consider this an unusual value.

When the responses were obtained from those who decided to respond a survey posted on the internet we have some problems associated to the sampling frame, since we are not considering all the possible individuals in order to take the sample of interest, we can have undercoverage and associated bias in the results.

Step-by-step explanation:

For this case we have the following data given:

162 respondents say that they never use a credit card

1217 say that they use it sometimes

2836 say that they use it frequently

So then the total os participants for this survey is:

162+1217+2836 = 4215

And we want to calculate the probability that a randomly selected person uses a credit card frequently. Using the definition of probability we got this:

For this case this probability represent more than 50% of the participants, so we can't consider this an unusual value.

When the responses were obtained from those who decided to respond a survey posted on the internet we have some problems associated to the sampling frame, since we are not considering all the possible individuals in order to take the sample of interest, we can have undercoverage and associated bias in the results.