Health officials routinely check the sanitary condition of restaurants. Assume you visit a popular tourist spot and read on social media that in 3 out of every 7 restaurants checked, unsatisfactory health conditions were found. Assuming you are planning to eat out 10 times while you are there on vacation, answer the following questions.
1. How likely is it that you will eat at three restaurants with unsanitary conditions?
2. How likely is it that you will eat at four or five restaurants with unsanitary conditions?
3. Explain how you would compute the probability of eating in at least one restaurant with unsanitary conditions. Could you use the complement to solve this problem?
4. What is the most likely number to occur in this experiment?
5. How variable will the data be around the most likely number?
6. How do you know that this is a binomial distribution?
7. If it is a binomial distribution, does that mean that the likelihood of a success is always \(50 \%\) since there are only two possible outcomes?
Check your answers by using the following computer-generated table.

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Mean = 4.29 Std. dev. 1.56492 X P(X) Cum. prob. 0123456789 0.00371 0.00371 0.02784 0.03155 0.09396 0.12552 0.18792 0.31344 0.24665 0.56009 0.22199 0.78208 0.13874 0.92082 0.05946 0.98028 0.01672 0.99700 0.00279 0.99979 10 0.00021 1.00000