Ch4
#1. Relative Frequency Probabilities.
Number of days stayed(X) Frequency(f)
3
15
4
32
5
56
6
19
7
5
#2.
Px
0.118110
0.251969
0.440945
0.149606
0.039370
Simulate 50 births, where each birth results in a boy or girl.
Tally for Discrete Variables: C1
C1
0
1
N=
Count
29
21
50
Percent
58.00
42.00
a) 21Girls(Answers vary.) 1s for baby girls and 0s for baby boys
b) 21/50=42
c) No, 0.5 is only the theoretical probability. As the number of trials increases, the
empirical probability of an event will approach the theoretical probability.
#3. a)
C2
2
3
4
6
N=
Count
1
1
1
2
5
Percent
20.00
20.00
20.00
40.00
Tally for Discrete Variables: C3
b)
C3
1
2
3
4
5
6
N=
Count
6
4
5
1
5
4
25
Percent
24.00
16.00
20.00
4.00
20.00
16.00
c)
Tally for Discrete Variables: C4
C4
1
2
3
4
5
6
N=
d)
Count
10
11
6
8
6
9
50
Percent
20.00
22.00
12.00
16.00
12.00
18.00
Tally for Discrete Variables: C5
C5
1
2
3
4
5
Count
22
15
11
13
23
Percent
22.00
15.00
11.00
13.00
23.00
1
6
N=
16
100
16.00
e)
Tally for Discrete Variables: C6
C6
1
2
3
4
5
6
N=
Count
81
74
74
84
105
82
500
Percent
16.20
14.80
14.80
16.80
21.00
16.40
(Extra for N=1000)
Tally for Discrete Variables: C7
C7
1
2
3
4
5
6
N=
Count
160
154
167
168
177
174
1000
Percent
16.00
15.40
16.70
16.80
17.70
17.40
f) Law of large numbers: when a probability experiment is repeated a large number of times, the relative frequency probability of
an outcome will approach its theoretical probability.
Ch5
#1. Calculating Binomial Probability
Binomial with n = 20 and p = 0.05
x
5
P( X = x )
0.0022446
(0.002 using the binomial distribution table)
2.
Constructing a binomial Distribution
a.
Binomial with n = 20 and p = 0.63
X
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
P(X)
0.000000
0.000000
0.000001
0.000013
0.000094
0.000513
0.002184
0.007437
0.020578
0.046719
0.087503
0.135446
0.172969
0.181240
0.154299
0.105090
0.055918
0.022403
0.006358
0.001139
0.000097
2
b. P(at least 10 are employed outside the home)= P(X=10)+ P(X=11)+ P(X=12)+ P(X=13)+ P(X=14)+
P(X=15)+ P(X=16)+ P(X=17)+ P(X=18)+ P(X=19)+ P(X=20)= 0.922462
3.
a.
X
0
1
2
3
4
P(X)
0.12
0.20
0.31
0.25
0.12
Mean
2.05
SD
1.18638
b)
Binomial Distribution n=20, p=0.63
Yoon Yun
0.30
P(X)
0.25
0.20
0.15
0.10
0
1
2
X
3
4
Ch6
1. Central Limit Theorem
a. C26
b.
Histogram (with Normal Curve) of SM
Mean
StDev
N
40
56.01
2.262
200
Frequency
30
20
10
0
50
52
54
56
SM
58
60
62
Yes, it appears to be normally distributed.
c.
Descriptive Statistics: SM
Variable
SM
N
200
Variable
SM
Maximum
62.042
d.
N*
0
 x  2.262
Theorem,
2.
SE Mean
0.160
StDev
2.262
Minimum
50.125
Q1
54.564
Median
56.147
Q3
57.455
 x  56.021
Yes, it is close to
e.
Mean
56.012
x 
  56 .
No, it is not close to
yes, according to the Central Limit Theorem,
  12 .

However, it is close to

n

x  
12
 2.4 . According to the Central
25
Limit
n
Cumulative Distribution Function
3
Normal with mean = 0 and standard deviation = 1
x
1.39
P( X <= x )
0.917736
3. Inverse Cumulative Distribution Function
Normal with mean = 0 and standard deviation = 1
P( X <= x )
0.025
x
-1.95996
4