Probability Assignment | Answers

Surname 1
Name:
Instructor:
Course:
Date:
Question 1
p ( t ) =P. of transfering a ball
p ( t ) = r1
n1
p ( g ) =P . of picking ¿ ball ¿ urn 2 after transfering a ball= r 2
n2+1
Therefore
probability of picking a ¿ ball= ( r1
n1 )× ( r2
n2 +1 )= r 1 r2
n1( n2+ 1)
Question 2
a.
For probability mass function (pmf);
∑ p ( xi ) =1
p ( xi )> 0
f ( x )= x +2
c , x=1,2,3 , ... ... ... 15
So ∑ p ( xi ) =1 50
150
C =1
C=150

Surname 2
b.
Number of copies sold in a year
∑ p ( xi ) =150
150 Copies
c.
Profit for the year
Profit from each book is $10. So total profit;
Total profit=$ 10 ×150
Total profit=$ 1500
Question 3
The exponential function , f ( x )=λ e− λ x
λ= 1
15 =0.067
p ( x>12 ) =0.067 e−0.067(12)
p ( x>12 ) =0.03
Question 4
a. Two standard deviation about the mean of 10 is 9.8
p ( x ; μ )= e− λ λx
x !
p ( 9.8 ; 10 )= e−10 1010
10 !
p ( 9.8 ; 10 )=0.125
b.
p ( x ; μ )= e− λ λx
x !
p ( 5 ;10 )= e−10 105
5 !

Surname 3
p ( 5 ;10 )=0. 038
c.
p ( x ; μ )= e− λ λx
x !
p ( 10.67 ; 10 )= e−10 1010.67
10.67 !
p ( 10.67 ; 10 )=0.0 .12
Question 5
a.
Sample proportion
proportion= 0.0915+ 0.3085
2 =0.2
proportion=0.2
b.
margin of error=0.3085−0.2
margin of error=0.1085
But
margin of error=zα /2 √ ^p ( 1− ^p )
n
0.1085=zα / 2 √ 0.2 ( 1−0.2 )
50
0.1085=zα / 2 √ 0.2 ( 0.8 )
50
0.1085=zα / 2( 0.0565685)
zα/ 2= 0.1085
0.0565685
zα/ 2=1.92