Test 8:  Probability and statistics

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MQ6 TEST 8A  (answers below)                                                                                      Mr. Gary Jaye

INSTRUCTIONS: 1. Express all answers in simplest form , SHOW ALL WORK, and box answers.
                                        2. NO graphing calculators     3. Use pen (except for graphs)

1. In a-c, apply the Law of Sines or the Law of Cosines to triangle RST.          [3 each]
a. If r, s, and t
    are known, cos T =		 b. If s/r = 2/3, another ratio that equals 2/3 is
    (do NOT give a numerical answer like 4/6):
c. If s, t and <R are known, r2 =

 

 

 

 

 

 

2. In a-c, fill in the answer.           [3 each]
a. If nC7 = nC2, then n equals: b. The number of permutations of MOOMOO
     involving every letter is:
c. State symbolically, the probability of drawing (without replacement )
    a 5-card hand of 2 queens and 3 kings from a standard deck of 52 cards.

 

 

 

 

 

 

3. A club consists 5 seniors and 6 juniors. Fill in the symbolic and numerical answer for each question.  [4, 4, 6]
a. Find the number of  presidential/vice-
    presidential/treasurer slates that can be
    formed.		 symbolic answer:

 

 numerical answer:

 
b. Find the number of 4-person delegations
    that can be formed. 		symbolic answer:
 numerical answer:
c. Find the number of committees consisting      of  3 seniors and 4 juniors that can be        formed. symbolic answer:
 numerical answer:

 

 

 

 

 

 

 

 

 

 

4. A biased coin, for which p(heads) = 2/3, is tossed 4 times. In a-d, express the indicated probability  symbolically and as a fraction in simplest form. Box your answers. [3, 3, 3, 4]
a. p(2 heads)

 

 
b. p(3 heads)

 

 
c. p(4 heads)

 

 
d. p(at least 3 heads)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. Find the 6th term in the expansion of (2x - y)8 and show work. [10]

 

 

 

 

 

 

 

 

 

 

6. In a standardized test with a normal distribution of scores, the mean is 62 and the standard deviation is 5.
a. Which score can be expected to occur most often?
    (1) 44    (2) 58    (3) 68     (4) 72    (5) 74                  ANSWER:                                                                [3]
b. If x represents a score, the probability that 67 £ x £ 72 is:                                                                            [3]

 

 

 

 

 

 

7. The table below shows the grades for a college statistics class. In a-d, answer to the nearest tenth. [2, 3, 4, 8]

Grade

Frequency
92 2
87 3
82 6
77 9
72 10 
67 6
62 6

      a. The mode is:

      b. The mean is:

      c. The median is:

      d. The standard deviation is:

 

 

8. Simplify (1 - i)8 and show work. [6]

 

 

 

 

 

 

 

 

 

9. Solve the equation cos2q + cosq +1 = 0 for q in the interval 0° £ q < 360° to the nearest tenth and
    show work. [13]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANSWERS:  1a. cos T = (r2 + s2 - t2)/(2rs)     1b. s/r = sin S/sin R    1c. r2 = s2 + t2 - 2st cos R     2a. n = 9
2b. 6!/(4!2!) = 15    2c. (4C2 × 4C3)/52C5     3a. 11P3 = 990     3b. 11C4 = 330    3c. 5C3 × 6C4 =  150
4a. p(2H) = 4C2(2/3)2(1/3)2 = 8/27    4b. p(3H) = 4C3(2/3)3(1/3)1 = 32/81    4c. p(4H) = 4C4(2/3)4(1/3)0 = 16/81
4d. p(at least 3H) = 4C3(2/3)3(1/3)1 + 4C4(2/3)4(1/3)0 =   32/81 + 16/81 = 16/27    5. 8C5(2x)3(-y)5 = -448x3y5
6a. (2) 58    6b. p = .135    7a. 72    7b. 75    7c. 74.5    7.9     8. 16    9. {90°, 120°, 240°, 270°}

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