1.A small pizza shop, which is only open at lunchtime, has only eight toppings available. They also have a selection of 3 beverages.

2. How many ways can five of the 8 different topping bins be arranged in a row on the work counter?

3. The Super Saver is a $6 meal deal. For just $6 you can have your choice of any 1-topping pizza or a plain pizza without any toppings, and you can have any one of the three beverages. If you eat lunch at this pizza shop everyday and you like variety, then for how many days can you consume a different Super Saver meal deal until you have to repeat a particular pizza with a particular beverage?
For Problems 4-7, refer to the following information.

The times taken to complete Quiz #2 in STAT 200 appear to be normally distributed with a mean of 106 minutes and a standard deviation of 15 minutes.
4. Find the probability that a randomly selected STAT 200 student takes at most 120 minutes to complete Quiz #2.

5. Find the probability that a randomly selected STAT 200 student takes over 106 minutes to complete Quiz #2.

6. Thirty-three percent of STAT 200 students complete Quiz #2 in less than how many minutes?

7. Sixteen STAT 200 students, who completed Quiz #2, are randomly selected. The mean amount of time they took to complete Quiz #2 was 97 minutes. Find the z-value that corresponds to this sample mean.
For Problems 8-12, refer to the following information.

According to a past U.S. Census, approximately 20% of U.S. Americans who are age 65 or older have completed 4 or more years of college. For a group of 15 randomly selected U.S. Americans, who are age 65 or older, answer the following.
8. Find the probability that exactly six of those 15 people have completed 4 or more years of college.

9. Find the probability that at least one of them has completed 4 or more years of college.

10. For this sample of 15 U.S. Americans, find the mean number to have completed 4 or more years of college.

11. Find the standard deviation for this distribution.

12. Check this binomial distribution to see whether it can be reasonably approximated by a normal distribution. State either 'Yes, it can' or state 'No, it cannot' and support your answer with numerical evidence.
For Problems 13-16, refer to the following information.

The following chart is based upon the status (freshman, sophomore, junior, senior/post-bacc) of the students who are enrolled in our section of STAT 200.

Status

Gender Freshman Sophomore Junior Senior/Post-Bacc Totals

Male 4 0 4 3 11

Female 2 0 5 2 9

Totals 6 0 9 5 20
If one of these 20 students is randomly selected, then
13. Find the probability that the student selected is a junior or is a male.

14. Find the probability that the student selected is a female given that the student is a freshman.

15. Find the probability that the student selected is a post-bacc male.

16. Find the probability that the student selected is not a sophomore.
For Problems 17 and 18, refer to the following information.

A bakery sells frittelle (filled doughnut holes) that are dipped in chocolate, which externally makes all of them look identical. Assume too that weight-wise they all feel identical. You purchased five that are filled with vanilla cream, seven pistachio pudding filled, ten lemon custard, and four that are filled with apricot jam. The baker put all of the frittelle you purchased into one box and by the time you reach your destination the frittelle are well rearranged in the box in a random manner due to the jostling of the box.
17. If one of the frittelle in this box is randomly selected, what is the probability that it is filled with vanilla cream or with pistachio pudding?

18. If three of these frittelle are randomly selected, one at a time and eaten as selected, what is the probability that all three are filled with lemon custard?

Let X be the number of letters in Scrabble words that contain a ‘q' but not a ‘u'. This distribution is shown below. Remember to express your answers, as appropriate, in reduced fractional form or rounded to the nearest hundredth or thousandth or to the nearest tenth of a percent.

Number of Probability

Letters, X P(X)

2 ?

3 0.06

4 0.14

5 0.31

6 0.46
19. In order for this distribution to qualify a probability distribution, what must the value of P(2) be? In other words, what number must replace the question mark in the distribution given above in order for this distribution to qualify as a probability distribution? Note: if you don't know the answer then guess an answer and use it, if need be, when answering the following two problems.

20. Find the mean for this distribution.

21. Find the variance for this distribution.