Statistics and Probability

Running Head: Statistics and Probability
Statistics and Probability Assignment
Student’s Name
Institution Affiliation

Statistics and Probability
Question One
a. Graphical Display
i. The graphical display is dot plot. The similarity is that on both graphs, most values lie
between 135 and 140. The difference is that on the first graph there are outliers
whereas in the second one there are none.
ii. To maximize the probability of having the Ping-Pong balls land within the band,
parents will prefer catapult B to A, since catapult A has more variability than B as
revealed by the presence of outliers in its distribution.
iii. The catapult B should be placed 138 centimeters from the target line. This is because
the 138 is approximate to the target and it’s within the range of most values (135 to
140).
b. Stem-and-Leaf Display
To do Stem-and-Leaf display the data values were arranged in ascending order from the
minimum to maximum (Black, 2009). In our, case from 125 to 164.The display is given below.
Stem Leaf
12 5 6 6 6 6 6 7 9 9 9
13 0 0 0 1 1 2 2 2 2 2 3 5 6 6 7 9
14 0 2 5 5 5 6 6 6 7 8
15 2 5 6
16 4
From the display, it’s clear that most values of the data are on the second stem (13). Also, the
distribution is not asymmetrical as most values lie on the lower side (smaller stems, 12 and 13)

Statistics and Probability
Question Two
a. Parking tickets
The probability that a driver gets at least one parking ticket yearly ( p ) is 0.06
i. Binomial model and Poisson to Binomial distribution
According to Francis and Mousley (2014), Binomial model is given by;
P ( X=k ) = ( n
k ) pk ( 1−p ) n−k
where,
n=sample ¿ 80
p= probability of sucess=0.06
k =number of successful events
Therefore, the probability that 4 drivers get at least one parking ticket will be,
P ( X=4 )=(80
4 ) ( 0.06 )4 ( 0.94 )76
¿ 0.186
Poisson approximation to Binomial
According to Ross (2014), to approximate Poisson to Binomial the terms of binomial and
Poisson model are related by the formula;
p= λ
n
Where,
p=term form binomial model ,
λ=average term ¿ Poissonmodel ,

Statistics and Probability
n=sample ¿ ¿
Therefore,
p= λ
n
0.06= λ
80
λ=4.8
According to Borradaile (2013), from this figure, the Poisson is approximated to Binomial by the
e−λ λk
k ! =(n
k ) ( λ
n )k
(1− λ
n )n−k
Therefore,
P ( X=4 ) = e−4,8 ( 4.8)4
4 ! =0.1820
This probability is less than the one computed using binomial model.
ii. By Poisson approximation to Binomial distribution the probability that at least 3 driver
will get at least one ticket
P ( X ≥3 )=1− {P ( 0 )+ P ( 1 ) + P ( 2 ) }
P ( 0 )= e−4,8 ( 4.8 )0
0 ! =0.0082
P ( 1 ) = e−4,8 ( 4.8 ) 1
1 ! =0.0395
P ( 2 ) = e−4,8 ( 4.8 )2
2 ! =0.0948
P ( 3 ) = e−4,8 ( 4.8 ) 3
3! =0.1517