STATISTICS 200 MIDTERM EXAM
NAME:
Kim, Mo Se
1.
This is an open book exam.
2.
Plan to spend one hour to complete it.
3.
Submit your completed exam into the assignment folder MT (midterm)
1.
Calculate the probability of having 14 girls in 14 children.
Write your formulae
neatly to show ALL the steps and place the answer in scientific notation.
(10 points)
G = A girl
P(G) =
1/2 = 0.5
P(all 12 girls) = P(G1 and G2 and G3 and ……. G13 and G14)
= P(G1) x P(G2) x P(G3) …… x P(G13) x P(G14)
=
(0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5)
= (0.5)^14
= 0.00006103515625
In Scientific notation this is 6.103515625 x 10^5
2.
Solve the permutation and combination using the formulas supplied. (10 points)
Formulas
3!= (3)(2)(1)
!
(
)!
n
r
n
P
n
r
=

!
(
)! !
n
r
n
C
n
r
r
=

25
P
4
25!/(254)! = 25!/21! = (25)(24)(23)(22) = 303600
53
C
2
(53)!/{(532)!2!} = 53!/{(2)!(5!)} = {(53)(52)} / {(2)(1)} = 2756 / 2 = 1378
3. Determine the probabilities of blood groups using the chart below.
Show all your
work. (15 points)
Group
O
A
B
AB
TOTALS
Rh class
Rh+
39
35
8
4
86
Rh class
Rh
6
5
2
1
14
Totals
45
40
10
5
100
P(Rh)
P(Rh) =14/100 = 0.14
P(A)
P(A)=40/100 = 0.4
P(Rh+)
P(Rh+)=86/100 = 0.86
P(A and Rh+)
P(A and Rh+) = (From the chart) 35/100 = 0.35
P(A or Rh+)
P(A) + P(Rh+) – P(A and Rh+) =
0.40 + 0.86 – 0.35 = 0.91
4. Find the age of the actress in the chart on page 130 of your text using the percentile
given and the locator formula
L = (k/100) x n,
where n = 76
(5 points)
Percentile
Calculation for the position of the actress in the chart
Age
P
10
L = (10/100)76 = 7.6
8
∴
th
25
P
66
L=
(66/100)76 = 50.16
51th
∴
37
P
75
L=
(75/100)76 = 57
(39+40)/2 = 39.5
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 Spring '09
 MoSeKim
 Statistics, Probability, Standard Deviation, Summation, Chocolate Chip, Diet Pepsi

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