1. How many different 7-letter codes can be formed by using all the letters of INDIANA?
(A) 8!
(B) 7!
(C) 7!/8
(D) 8!/7
(E) 7!/2!
(F) none of the above
2. Randomly selected 10 students in a class earned the following scores in a test: 33 75 87 88 99 93 87 85 72 25 Find the five-number summary.
(A) (25, 73.5, 86, 87.5, 99)
(B) (25, 72, 86, 88, 99)
(C) (33, 87, 95, 85, 25)
(D) (25, 72, 85, 88, 99)
(E) not enough information to compute
(F) none of the above
3. Find the mild and extreme outliers of the scores given in previous problem.
(A) 25 and 99 are the only extreme outliers
(B) 25 is the only extreme outlier
(C) both 25 and 33 are extreme outliers
(D) both 25 and 33 are mild outliers
(E) 25 and 99 are the only mild outliers
(F) none of the above
4. Find the trimmed mean x¯tr (15) up to two decimal places for 10 scores given in problem 2.
(A) 74.40
(B) 82.33
(C) 77.50
(D) 79.92
(E) 86.00
(F) none of the above
5. Suppose that the sample mean x¯ and standard deviation s of 10 scores in problem (2) are calculated as x¯ = 74 and s = 25.22 (approximated to two decimal places). If the test scores are curved using the formula 2.5x + 10 where x is the actual score, calculate the sample mean and standard deviation of the 10 scores after the curve.
(A) (195, 73.05)
(B) (185, 63.05)
(C) (185, 73.05)
(D) ((195, 63.05)
(E) ((84.4, 35.22)
(F) none of the above
6. A box contains three green balls, four yellow balls and five red balls. Three balls are randomly selected simultaneously from this box. Find the probability that all three selected balls are green.
(A) 1/60
(B) 1/110
(C) 1/220
(D) 1/255
(E) 1/330
(F) none of the above
7. Find the probability that all three selected balls in the previous problem are of same color.
(A) 3/44
(B) 1/40
(C) 1/220
(D) 3/220
(E) 1/60
(F) none of the above
8. A box contains three green balls and four yellow balls. If three balls are randomly selected one after another without replacement, find the probability that two balls of same color are not selected in a row.
(A) 2/7
(B) 6/7
(C) 1/12
(D) 1/7
(E) 1/35
(F) none of the above
9. Which one of the following statements is TRUE?
(A) Sample mean and median are always different from each other
(B) Sample median is always the best measure for center
(C) Standard deviation is not a resistant measure
(D) Sample mean and median are always equal
(E) Changing every value of a sample to its negative will always change the standard deviation from s to -s.
(F) All these above statements are true
10. The grade distribution of a large statistics class was as follows: 15% received A grade, 30% received B grade, 10% received C grade, 30% received D grade, and 15% received F grade. Then the histogram of this date for the categorical variable 'grade':
(A) is strongly right skewed
(B) is strongly left skewed
(C) is unimodal
(D) is bimodal
(E) has an extreme outlier
(F) none of the above
11. If a fair coin is tossed four times, find the probability that at most one of the toss is head.
(A) 5/16
(B) 5/8
(C) 1/4
(D) 1/16
(E) 11/16
(F) none of the above
12. In a science undergraduate class, 10% of students were freshmen, 20% were sophomore, 30% were juniors, and 40% were seniors. At the end of the semester, 70% of freshmen, 75% of sophomore, 80% of juniors and 85% of seniors passed the course. If a randomly selected student from this class passed the course, find the probability that the selected students was a sophomore.
(A) 3/16
(B) 3/8
(C) 1/10
(D) 4/5
(E) 1/5
(F) none of the above
13. If 40% of IU students like calzone, 65% like pizza and 80% like either calzone or pizza, what percent of IU students like both calzone and pizza?
(A) 0.2
(B) 0.25
(C) 0.6
(D) 0.35
(E) 0.4
(F) none of the above
14. In previous problem, what percent of IU students like pizza but not calzone?
(A) 0.2
(B) 0.25
(C) 0.6
(D) 0.35
(E) 0.4
(F) none of the above
15. In a survey of 100 people, 45 liked romantic movies, 48 liked mystery movies, 50 liked action movies, 30 liked both romantic and mystery movies, 25 liked both romantic and action movies, 20 liked all three type of movies and 15 do not like any of these movies. How many liked both mystery and action movies?
(A) 3
(B) 23
(C) 15
(D) 19
(E) 17
(F) none of the above
16. You randomly select 4 cards from a well shuffled deck of standard 52 cards. Find the prbability that at least one of them is an ace.
(A) 4!/52!
(B) C1,52/C4,52
(C) 1 -C4,48/C4,52
(D) 1 -P1,52/P4,52
(E) C4,48/C4,52
(F) none of the above
17. You randomly selected 10 cards from a standard deck of cards and noticed that exactly four of them are red cards. After shuffling these 10 cards well, you again randomly select 6 cards out of these 10 cards. What is the probability that exactly two of these six cards are red?
(A) 1/3
(B) 2/5
(C) 2/3
(D) 3/5
(E) 3/7
(F) none of the above
18. You have ten songs in your Ipod and exactly three of them are Beatles songs. If you make a playlist of these 10 songs in an album, what is the probability that the first Beatles song listed in your playlist is the third song?
(A) 3/10
(B) 7/10
(C) 7/40
(D) 3/40
(E) 3!/10!
(F) none of the above
For next two problems, write all your steps clearly and write your answer as an exact simplified fraction (NOT as a decimal) on the front page;
19. An employee of Registrar's office has ten requests on his computer awaiting to process. Six of these requests are course add and other four are course drop requests. If he randomly selected six of these requests and processed, what is the probability that only one of the two types of requests remains on his computer?
20. Adam and Eve are in M118 class. Let A denote the event that Adam receives A grade in M118 and E represent the event that Eve receives A grade in M118. If A and E are independent events with P(E) > P(A), P(A ∪ E) = 0.7 and P A ∩ E) = 0.2, determine P(A) and P(E).
Hint: If ax 2 + bx + c = 0, then x =
-b ±
√b2 - 4ac2a
(quadratic formula)