1. The following data represents the lengths of long distance phone calls (in minutes).
1 6 15 9 17
6 8 10 24 14
a) Find the range, sample mean, mode and median.
b) Find the sample variance and standard deviation.
2. Suppose it is known that verbal SAT scores have a bell-shaped distribution with a mean of 500 and a standard deviation of 100.
a) What percentage of verbal SAT scores are between 400 and 700?
b) What percentage of verbal SAT scores are less than 300 and more than 800?
3. Lengths of long distance phone calls (in minutes):
0.8 42.02 20.6 2.8
36.7 18.6 23.3 11.5
3.7 14.9 9.4 1.5
14.9 31.1 23.5 9.5
a) Which time represents the 82nd percentile
c) What is the percentile of a time of 11.5 minutes?
4. Chloe puts a coin into a gumball machine that contains 12 blue, 15 pink, 9 orange, 16 yellow, and 14 white gumballs. What is the probability that Chloe gets a yellow gumball?
5. Roll a pair of dice, what is the probability of rolling an even total or a total greater than 9?
6. In a class of 35 students,
a) How many ways can a teacher place 8 students on the front row?
b) How many ways can a teacher choose a class president and vice-president?
7. In how many ways can the letters in the word ‘statistics' be arranged?
8. A family is planning their vacation. Each of the five family members is allowed to nominate three places they would like to visit. If they want to visit 4 different places during the trip, in how many ways can they plan their road trip assuming no family members choose the same place?
9. Ashley loves to play the floating duck game at the carnival. For $2.00 per try, you get to choose one duck out of the 50 swimming in the water. If he is lucky, he will pick one of the 8 winning ducks and go home with a pink teddy bear.
a) What is the expected value of the game, if the value of the prize is $5.00?
b) If Ashley plays the game 10 times, how much can she expect to win or lose?
10. At one university, freshmen account for 30% of the student body. If a group of 10 students is randomly chosen by the school newspaper to comment on textbook prices, what is the probability that more than 3 of the students are freshmen?
11. On average, Patrick sees a spider in his home once a month. What is the probability that Patrick sees no more than one spider in a month and a half?
12. Jay has 10 pieces of mail to open, 4 of which are junk mails. What is the probability that he randomly opens 2 pieces of mail and they are both junk mail?
13. One southern city experiences an ice storm on average once every eight years. Calculate the probability that there is an ice storm in the city twice in the next three years.
14. You forgot to study for history exam, and you don't know the answers to any of the 10 questions on the page. If each question has 4 multiple choice options (one of which is correct), what is the probability that you will guess the right answer on at least one question?
15. Every time Brietta goes to the mall, she has a 0.6 chance of forgetting where she parked her car. If she goes to the mall 5 times this month, what is the probability that she will forget where she has parked less than 2 times?
16. Find each specified probability.
a) P(z<-3.14) b) P(z>-0.81) c) P(-1.861.26)
17. The total blood cholesterol levels in a certain Mediterranean population are found to be normally distributed with a mean of 160 milligrams/deciliter (mg/dL) and a standard deviation of 50 mg/dL. Researchers at the National Heart, Lung, and Blood Institute consider this pattern ideal for a minimal risk of heart attacks.
a) Find the percentage of this population who have blood cholesterol levels between 150 and 200 mg/dL.
b) Find the percentage of this population who have blood cholesterol levels less than 100 mg/dL or greater than 220 mg/dL.
18. Find the indicated value of z.
a) What z-value has an area of 0.5987 to its right?
b) Find the value of z such that the area to the left of -z plus the area to the right of z is 0.5686.
19. Suppose that the diameters of oak trees are normally distributed with a mean of 4 feet and a standard deviation of 0.375 feet.
a) What is the probability of walking down the street and finding an oak tree with a diameter of more than 5 feet?
b) What is the probability of sampling a set of 87 oak trees and finding their mean to be more than 4.1 feet in diameter?