Faculty of Computer Studies Course Code: M130 Course Title: Introduction to Probability and Statistics Tutor Marked Assignment Cut-Off Date: Total Marks:60 Contents Question 1……………………..………………………………………..……… 3 Question 2……………………………..………………..………………

Faculty of Computer Studies
Course Code: M130
Course Title: Introduction to Probability and Statistics
Tutor Marked Assignment

Cut-Off Date: Total Marks:60

Contents
Question 1……………………..………………………………………..……… 3
Question 2……………………………..………………..……………………… 3
Question 3………………………………..………………..…………………… 4
Question 4………………..……………………………………..……………… 4
Question 5……………………………………………………………………… 5
Question 6……………………………………………………………………… 5

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QUESTION 1 2 3 4 5 6
MARK 10 10 10 10 10 10
SCORE
TOTAL




Tutor’s Comments:


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: [3+2+2+3 Marks] A dietitian is interested in comparing the sodium content of real cheese with the sodium content of cheese substitute. The data for two random samples are shown.
Real cheese 310 420 45 40 220 240 180 90
Cheese substitute 270 180 250 290 130 260 340 310


Find the sample mean and the sample median for each group.
Find the range and the interquartile range for each group.
Find the sample standard deviation .
Compare the distributions, using parts b and c.

Q-2: [2+2+2+2+2 Marks]
Suppose a business owner has a choice of 5 locations in which to establish her business. She decides to rank each location according to certain criteria, such as price of the store and parking facilities. How many different ways can she rank the 5 locations?
A school musical director can select 2 musical plays to present next year. One will be presented in the fall, and one will be presented in the spring. If she has 9 to pick from, how many different possibilities are there?
A newspaper editor has received 8 books to review. He decides that he can use 3 reviews in this newspaper. How many different ways can these reviews be selected?
Find the number of permutations that can be formed from the letters INFINITY?
In how many ways can 5 different trees be planted in a circle?

Q-3: [3+2+2+3 Marks] A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities.

Exactly 2 are defectives.
None is defective.
All are defective.
At least 1 is defective.

Q-4: [3+3+4Marks] In an experiment to study the relationship of hypertension and smoking habits, the following data are collected for 180 individuals:
Nonsmoker Moderate Smoker Heavy Smoker
H 21 36 30
NH 48 26 19

Where H and NH in the table stand for Hypertension and No hypertension, respectively. If one of these individuals is selected at random, find the probability that the person is:
Experiencing hypertension ,given that the person is a heavy smoker;
A non-smoker, given that the person is experiencing no hypertension;
Determine if the events experiencing hypertension and the person is heavy smoker are independent events. Show your work!

Q-5: [3+2+3+2 Marks] The random variable X, representing the number of errors per 100 lines of software code, has the following probability distribution:
X 2 3 4 5 6
P(X)=F(X) 0.01 0.25 0.4 0.3 0.04


a)Find The cumulative distribution of the random variable x .
b) Find the mean of the random variable X.
c)Calculate the variance and standard deviation of the random variable X.
d)What is the probability that the number of errors per 100 lines of software code are 3 or more .



Q-6: [3+2+2+3 Marks] For a laboratory assignment, if the equipment is working, the density function of observed outcome X is f(x) = 2(1-x), 0 < x< 1
0 otherwise

Find the cumulative distribution function F(x) of x.
Compute p( 1/4 ≤x ≤ 1/2).
Find the mean of the random variable x.
Find the standard deviation of the random variable x.