MDM4U-Final Exam
Name: ______June 2003 Page 1 of 3
Mdm4u-Final Exam
Answer Section
MULTIPLE CHOICE
1. ANS: D
2. ANS: A
3. ANS: A
4. ANS: B
5. ANS: A
6. ANS: A
7. ANS: A
8. ANS: A
9. ANS: A
10. ANS: C
11. ANS: D
12. ANS: A
13. ANS: A
14. ANS: C
15. ANS: B
16. ANS: C
17. ANS: C
18. ANS: D
19. ANS: D
20. ANS: D
21. ANS: C
22. ANS: B
23. ANS: A
24. ANS: A
25. ANS: A
26. ANS:
Our student needs to guess at least 4 questions correctly from the 24 available. The mean of the normal approximation is 6 so we may apply it. Making the transition to a continuous variable, we need P(X < 3.5).
z = = –1.1785
The area under the curve for this z-score is 0.1193. Our student has almost a 12% chance of failing and therefore an 88% chance of passing the test.
27. ANS:
a) For the mean, .
For the standard deviation, .
Solve for x in the equation .
x = 121
b) There is a probability of 99.86% that we will observe 121 heads or fewer in 200 tosses of a fair coin.
28. ANS:
The general term for the expansion is = .
For the required term, 14 – 5r = –11, which provides r = 5 (the sixth term in the expansion).
The value of the coefficient is .
29. ANS:
From the general term of the expansion, we require = 0.1602.
30. ANS:
a) E(X) = 1(0) + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 5.18
The expected number of strokes for the hole is 5.18.
b) Most golfers are not good golfers. Unless the pro tour was visiting, we would not expect the average score for the hole to approach par.
31. ANS:
There are 3 possibilities = {2 red, 2 blue, 3 green}, {2 red, 3 blue, 2 green}, and {3 red, 2 blue, 2 green}.
Number of ways
32. ANS:
The probability is P(at least one of each is chosen)
33. ANS:
The probability is P(Julie and Tamar will not be next to each other)
34. ANS:
Let be the event of turning up a face card and a red four or five.
is 12 face cards 4 red fours or fives = 48.
is 52 cards ´ 51 cards 2 (order does not matter) = 1326.
35. ANS:
Therefore, 26 fish should have a mass more than 400 g.