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

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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: [2+2+2+4 Marks] the math and reading achievement scores from the National Assessment of Education Progress for selected states are listed below.

Math Reading

52 66 69 62 61 63 57 59 59

55 55 59 74 72 73 68 76 73 65 76 76 66 67 71 70 70 66 61 61 69 78 76 77 77 77 80

Compute the sample means for the math and reading scores.

Compute the sample medians for the math and reading scores.

Find the interquartile range for the math and reading scores.

Find the sample standard deviation for the math and reading scores and comment on the result.

Q-2: [3+3+4 Marks] 1) in how many different ways can a person gathering data for a market research organization select three of the 20 households living in a certain apartment complex if:

A person care about the order in which the households are selected.

A person does not care about the order in which the households are selected.

In how many ways can two paintings by Monet, three paintings by Renoir , and two paintings by Degas be hung side by side on a museum wall if do not distinguish between the paintings by the same artists?

Q-3: [3+3+4 Marks] a die is loaded in such a way that each odd number is twice as likely to occur as each even number.

Find probability of G, where G is the event that a number greater than 3 occurs on a single roll of the die.

Find probability of B, where B is the event that the number of points rolled is a perfect square.

Find the probability that it is a perfect square given that it is greater than 3.

Q-4: [2+2+2+4 Marks] consider the promotion status of male and female officers of a major metropolitan police force in the eastern United States. The police force consists of 1200 officers, 960 men and 240 women. Over the past two years, 324 officers on the police force have been awarded promotions.

The specific breakdown of promotion for male and female officers is shown in the following table:

Man Woman Total

Promoted 288 36

Not Promoted 672 204

Total

Let M=event an officer is a man

W=event an officer is a woman

A=event an officer is promoted.

If an officer is selected randomly from the 1200 police force officers find the probability that:

The randomly selected officer is a man and is promoted;

The randomly selected officer is a man and is not promoted;

The randomly selected officer is a woman and is promoted;

The officer is promoted given that the officer is man.

Q-5:[2+2+2+4] A concerned parents group determined the number of commercials shown in each of five children’s programs over a period of time.

Number of commercials X. 5 6 7 8 9

P(X) 0.2 0.25 0.38 0.10 0.07

Find the cumulative probability distribution of the number of commercials.

Use the cumulative distribution of the random variable X, to compute P (X< Cool, P ( 6 Find the mean for this probability distribution.

d) Find the variance and the standard deviation for this probability distribution.

Q-6: [3+4+3 Marks] the probability density function of the random variable X is given by :

f(x) ={█(@1/5 for2

Verify that the area under the curve is 1.

Find P(3 c) Find the expected value of the random variable X.