1. I have noticed that it always takes at least two minutes to serve a customer at the delicatessen counter in my local supermarket. A model for the random variable T which represents the time in minutes taken to serve a customer, is a probability density function. The cumulative distribution function of T is given by            F (t) = 1- (4/t²),             t≥2         Find the probability of customers whose service takesLess than three minutes;More than five minutes;Between four and 5 minutes. 
   
   

 

 

Faculty of Computer Studies
Course Code: M130
Course Title: Introduction to Probability and Statistics
Tutor Marked Assignment
Cut-Off Date: 25/8/2016
Marks:60 Total Contents
Question 1……………………..………………………………………..………
Question 2……………………………..………………..………………………
Question 3………………………………..………………..……………………
Question 4………………..……………………………………..………………
Question 5………………………………………………………………………
Question 6……………………………………………………………………… 3
3
3
4
4
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1 M130 TMA Feedback Form
[A] Student Component
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Group Number: [B] Tutor Component
Tutor Name: QUESTION 1 2 3 4 5 6 MARK 10 10 10 10 10 10 SCORE
TOTAL Tutor’s Comments: 2 The TMA covers only chapters 1, 2, 3 and 4. It consists of six questions for a total
of 60 marks. Please solve each question in the space provided. You should give
the details of your solutions and not just the final results.
Q−1: [2+3+4+1 Marks] A testing lab wishes to test two experimental brands of
outdoor paint to see how long each will last before fading. The testing lab
makes 6 gallons of each paint to test. The results (in months) are as follow:
The normal monthly precipitation (in inches) for these same 10 cities are as
follows:
Brand A
Brand B
10
35
60
45
50
30
30
35
40
40
20
24
a) Calculate the mean, and median of each group.
b) Compute the range and the inter-quartile range for each group.
c) Calculate the standard deviation for each group.
d) Which set is less variable? Q-2: [2+3+5 Marks] A company has 7 senior and 5 junior officers. It wants to form a
committee. In how many ways can a 4- officers committee be formed so that it is
composed of
a) Any 4 officers?
b) 3 senior officers and 1 junior officers?
c) At least 2 senior officers?
Q-3: [3+3+2+2 Marks] In a study to determine employee voting pattern in a recent
strike election, 1,000 employee were selected at random and the following tabulation
was made:
Salary Classification
Strike
Hourly(H)
Salary(S)
Salary+ Bonus (B)
Yes (Y)
400
180
20
No (N)
150
120
130
3 a) What is the probability of an employee voting to strike, given that the person is
paid hourly?
b) What is the probability of an employee voting to strike, given that the person
receive a salary plus bonus?
c) What is the probability of an employee being on straight salary(S)?
d) Are the events S and Y independent?
Q-4: [2+2+2+2+2 Marks] The probability mass function of a discrete random
variable X is given in the following table:
x
f(x) 0
0.05 1
0.05 2
0.1 3
0.35 4
0.35 5
0.1 a) Calculate P(2 < X < 5) .
b) Calculate the cumulative distribution function of X.
c) Use the cumulative distribution function to find P( X > 3) and P(2 ≤ X ≤ 4 ¿
d) Calculate the mean of the random variable X.
e) Calculate the variance of the random variable X.
Q-5: [3+3+4 Marks] Suppose that the random variable X has the following
distribution function:
X
1
4
6
10
F(x) 1/3 1/2 5/6 1
a) Find the probability distribution of the random variable X.
b) Find the expected value of the random variable X.
c) Find the standard deviation of the random variable X. 4 Q-6: [3+4+3 Marks] I have noticed that it always takes at least two minutes to serve a
customer at the delicatessen counter in my local supermarket. A model for the
random variable T which represents the time in minutes taken to serve a
customer, is a probability density function. The cumulative distribution function
of T is given by
F (t) = 1- (4/t ² ),
t ≥2
Find the probability of customers whose service takes
a) Less than three minutes;
b) More than five minutes;
c) Between four and 5 minutes. 5

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