Statistics Assignment - Desklib Online Library

This Statistics assignment covers topics like GDP per capita, unemployment rate, monthly unemployment rate, expected value, standard deviation, cumulative distribution function, confidence interval and sample proportion. It includes solved problems and graphs for better understanding.

Running Head: STATISTICS ASSIGNMENT
Statistics Assignment
Name of the Student
Name of the University
Course ID

1STATISTICS ASSIGNMENT
Table of Contents
Answer 1..........................................................................................................................................3
Answer a......................................................................................................................................3
Answer b......................................................................................................................................3
Answer c......................................................................................................................................4
Answer d......................................................................................................................................4
Answer 2..........................................................................................................................................4
Answer a......................................................................................................................................4
Answer b......................................................................................................................................5
Answer c......................................................................................................................................6
Answer d......................................................................................................................................7
Answer 3..........................................................................................................................................7
Answer a......................................................................................................................................7
Answer b......................................................................................................................................8
Answer c......................................................................................................................................8
Answer d......................................................................................................................................9
Answer 4..........................................................................................................................................9
Answer a......................................................................................................................................9
Answer b....................................................................................................................................10
Answer 5........................................................................................................................................10
Answer a....................................................................................................................................10
Answer b....................................................................................................................................11
Answer 6........................................................................................................................................11
Answer a....................................................................................................................................11
Answer b....................................................................................................................................12

2STATISTICS ASSIGNMENT
Answer 1
Answer a
Belgium
Denmark
France
Germany
Greece
Italy
Netherlands
Spain
Sweden
United Kingdom
0
5
10
15
20
25
30
35
40
45
36.3 36.4 33.9 36.1
28.5 29.5
41
29.8
38.2 35.1
GDP/Capita
Countries
GDP Per Capita
Figure 1: Per capita GDP for EU countries
Answer b
Two countries having highest unemployment rate are Spain (22.6%) and Greece (16.7%).

3STATISTICS ASSIGNMENT
Answer c
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
Monthly Unemployment Rate
2016 2017
Months
Unemployment rate
Figure 2: Comparison of monthly unemployment rate
Answer d
Year Jan Feb Mar Ap
r May Jun Ju
l Aug Sep Oct No
v Dec Average
2016 1.37
%
1.02
%
0.85
%
1.13
%
1.02
%
1.00
%
0.8
3%
1.06
%
1.46
%
1.64
%
1.69
%
2.07
% 1.26%
2017 2.50
%
2.74
%
2.38
%
2.20
%
1.87
%
1.63
%
1.7
3%
1.94
%
2.23
%
2.04
%
2.20
%
2.25
% 2.14%
Answer 2
Answer a
Sample mean=
∑
i=1
10
Xi
N
¿ 2+6+7+ 9+12+13+13+14+16+ 18
10

4STATISTICS ASSIGNMENT
¿ 110
10
¿ 11
Sample median= ( N
2 ) th
observation+ ( N
2 +1 )
th
observation
2
¿ 5th observation +6th observation
2
¿ 12+13
2
¿ 25
2
¿ 12.5
As mean is less than median the distribution is negatively skewed.
Answer b
Q1=( N +1)
4 thterm
¿ 11
4 th term
¿ 2.75 thterm 3 rd term
¿ 7
Q3= 3( N +1)
4 thterm

5STATISTICS ASSIGNMENT
¿ 3× 11
4 thterm
¿ 33
4 thterm
¿ 8.25 th term 8 thterm
¿ 14
Interquartile Rage ( IQR )=Q3−Q1
¿ 14−7
¿ 7
Lower limit of Outlier=Q1−1.5× IQR
¿ 7− ( 1.5× 7 )
¿ 7−10.5
¿−3.5
Upper limit of Outlier =Q3+1.5 × IQR
¿ 14+ (1.5 × 7 )
¿ 14+10.5
¿ 2 4.5
No observation in the given data set lies outside limit of the outliers. Therefore, any of the given
number cannot be considered as an outlier.

6STATISTICS ASSIGNMENT
Answer c
Variance=1
n ∑
i=1
10
( Xi −X )2
¿ 1
N ∑
i=1
10
Xi
2 −X2
¿ 1428
10 −112
¿ 142.8−121
¿ 21.8
Answer d
From the box plot, it is seen that lower quartile is more distant from median as compared
to upper quartile. This indicates the distribution is negatively skewed.
Answer 3
# of legitimate
emergency calls: X
01234
Probability: P(X=x)0.400.200.150.150.10
Answer a
Expected value of number of legitimate calls
E ( X ) =∑
i=0
4
Xi Pi
¿ ( 0 ×0.40 )+ ( 1× 0.20 ) + ( 2× 0.15 ) + ( 3 × 0.15 )+ ( 4 × 0.10 )
¿ 0+0.20+0.30+0.45+0.40

7STATISTICS ASSIGNMENT
¿ 1.35
Answer b
Standard deviation of the legitimate emergency calls
SD ( X ) = √ E ( Xi −E ( X ) )
2
¿ √ E ( Xi
2 ) −E2 ( X )
¿ √ ∑
i=0
4
Xi
2 Pi−E2 ( X )
¿ √ ( 02 ×0.4 ) + ( 12 × 0.20 ) + ( 22 × 0.15 ) + ( 32 ×0.15 ) + ( 42 × 0.10 )− (1.35 )2
¿ √ ( 0+0.20+ 0.60+0.45+0.40 ) −1.82
¿ √3.75−1.82
¿ √1.93
¿ 1.39
Answer c
Cumulative distribution function
#of
legitimate
emergency
calls: X
01234
Probability:
P(X=x)
0.400.200.150.150.10
Cdf P(X<x)0.40.60.750.91

8STATISTICS ASSIGNMENT
Answer d
The probability of having more than three legitimate emergency calls is 0.10.
Answer 4
Let X be the event of waiting to pass through immigration. The distribution of X is
normally distributed with mean being 22 and standard deviation is 5 minutes.
Answer a
The probability that a traveler will spend between 16 and 28 minutes waiting to pass
through immigration is given as
P [ 16 < X <28 ]
¿ P [ 16−22
5 < X−22
5 < 28−22
5 ]
¿ P [ −6
5 < z< 6
5 ]
¿ [ −1.2< z<1.2 ]
¿ Φ ( 1.2 )−Φ (−1.2 )
¿ Φ ( 1.2 )−1+Φ ( 1.2 )
¿ 2 ×Φ ( 1.2 )−1
¿ ( 2 ×0.8849 ) −1
¿ 1.7698−1
¿ 0.7698

9STATISTICS ASSIGNMENT
Answer b
The probability that the mean of waiting time to pass though immigration is less than 20
minutes is obtained as
P [ X <20 ]=P
[ X−22
5
√15
< 20−22
5
√15 ]
¿ P [ z ←1.55 ]
¿ Φ (−1.55 )
¿ 1−Φ ( 1.55 )
¿ 1−0.9394
¿ 0.0606
Answer 5
Answer a
Given that, mean (μ) = 105
Standard deviation (σ) = 30
Sample size (n) = 15
95% confidence interval for mean is obtained as
μ± Z0.95 × σ
√n
¿ 105 ±1.96 × 30
√15

10STATISTICS ASSIGNMENT
¿ 105 ±1.96 × 7.7460
¿ 105 ±15.1822
¿ 89.8178 , 120.1822
Answer b
From the computed confidence interval it can be concluded that population mean lies
between the two bound of 89.82 and 120.18. The 95% confidence interval thus suggests there
are 95 times confidence that true population mean lies in this range.
Answer 6
Answer a
Sample Proportion (P)= 190
500
¿ 0.38
Sample standard error= √ P (1−P )
n
¿ √ 0.38 ( 1−0.38 )
500
¿ √ 0.38 × 0.62
500
¿ √ 0.2356
500
¿ 0.0217

11STATISTICS ASSIGNMENT
99% confidence interval for population portion is obtained as
Sample proportion ± Z0.99 × Sample standard error
¿ 0.38 ± 2.576× 0.0217
¿ 0.38 ± 0.0559
¿ 0.3241 , 0.4359
Answer b
The confidence interval for population proportion indicates that in 99% cases proportion
of women who wear flats to work lies between 0.32 and 0.44.