The Following Data Shows the Favorite Soft Drinks of 15 FOB Foundation Students

PPS0025 Introduction to Probability and Statistics

ASSIGNMENT 1

Question 1

The following data shows the favorite soft drinks of 15 FOB foundation students:

a)Prepare a frequency distribution table for these data. Next, calculate the relative frequency (in fraction form) and percentage distributions (round off to 2 decimal places).

b)Sketch a bar graph for the data above.

Question 2

The following data shows the highest qualification of 60 staff in a company.

a)Prepare a frequency distribution table for the data.

b)Draw a bar graph for the frequency distribution.

Question 3

The quiz marks of 30 students from Foundation in Management are given as below:

a)Determine the number of classes by using Sturge’s formula.

(Hint: Round up the number of classes)

b) Determine the class width. (Hint: Round up the class width)

c) Construct a frequency distribution table by using the lowest quiz mark in the data

set as the starting point. Also, include the cumulative frequency for each class in

the table.

d) Draw an ogive for the cumulative frequency distribution.

e) From the ogive, determine the percentage of students:

i) score 49.5 mark or less in the quiz. ii) score 65.5 mark or more in the quiz.

Question 4

One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. A sample of 50 complaints concerning carpet installation was selected during a recent year. The data represent the number of days between the receipt of a complaint and the resolution of the complaint:

a) Construct a frequency (f), relative frequency (r.f.), percentage (%) and cumulative

frequency (CF) distribution table by taking 1 as the lower limit of the first class.

Note: Use the LOWER integer for the number of classes.

Round UP the class width to the nearest integer.

b) Construct an ogive for the cumulative frequency distribution of the data in part (a).

Hence, using the ogive, determine the percentage of complaints that took more than

42.5days to be resolved.

c) Calculate the mean, median, mode and the standard deviation of the GROUPED data

in part (a).

d) By comparing mean, median and mode, describe the shape of the distribution.

Question 5

a) The following distribution table shows the number of hours spent on Facebook per

day in a sample of 200 people.

i) Determine the midpoint (m), cumulative frequency (C.F.), and of

each class.

ii) Find the mean, median, mode, variance and standard deviation of these data.

b)Below is the Air Pollutant Index (API) reading in Melaka town for the past 7

days.

50 52 82 79 60 51 82

Find the mean, median, mode, range, variance and standard deviation of these data.

Question 6

A total of 250staffs in FCIareasked to determine their favorite car. The survey reveals the following information.

110 like Honda cars

97 like Toyota cars

107 like Protoncars

35 like both Honda and Toyotacars

x like both Honda and Protoncars

40 like both Toyota and Protoncars

13 like all the three cars

39 dislikes all the three cars

Let H be the event of Honda car, P for Proton car, and T for Toyota car.

a)Find the value of x.

b)Represent the above information in a Venn diagram with numerical values.

c)Find the number of staffs who like Toyota and Honda cars but dislike Proton car.

d)Find the number of staffs who like more than one car.

e)If a staff liked Toyota, what is the probability that the staff also liked Honda?

Question 7

A survey on the favorite food consist of burger, pizza and spagetthi is carried out in MMU. The following information shows the preference of 150 students:

11 prefer all the three food

35 prefer both pizza and spagetthi

28 prefer both burger and spagetthi

25 prefer both burger and pizza

71 prefer spagetthi

77 prefer pizza

x prefer burger

Let B be the event of burger, S for spagetthi and P for pizza.

a) Represent the above information in a Venn diagram and find the value of x.

b) How many of the students who their preferences are of more than one of the food?

c)How many of the students prefer spagetthi or pizza but not burger? d) If one student is selected, what is the probability that the student has exactly two

preferences?

Question 8

a) During the Student Representative Council (SRC) committee election, each member

must elect a committee of five people from candidates consist of six boys and five

girls. Find the probability that the committee will have two girls and three boys if a

certain girl must be in the committee.

b) The student board consists of 32 students from 16 different majors with two students

from each major. A committee consisting of 4 students is to be formed.

1. How many different committees are possible?
2. How many committees are possible if the committee members should be from the different major?
3. If the committee is selected at random from all 32 students, what is the probability that the committee is formed from students with different major?

c) A team of 5 is chosen at random from 6 boys and 6 girls.

1. In how many ways can the team be chosen if there are no restrictions?
2. Find the probability that the team contains only two girls?

d) A group of kindergarten students which consists of eight boys and six girls, four

kindergarten students are selected to follow a trip to Zoo Negara so that at least threeboys are there in the trip. In how many ways can it be done?

e)In a company of 10 men and 8 women, how many ways can a committee of size 10

be chosen with 8 men and 2 women or 2 men and 8 women?

f)How many odd three-digit numbers can be formed from the digits 1, 2, 5, 6 and 9 if

each digit can be used only once?

g)A librarian chooses 5 Mathematics books, 3 Chemistry books, 4 Biology books and

8 English books from 8 Mathematics books, 7 Chemistry books, 9 Biology books

and 12 English books. How many different selections are there?

h)In a Mathematics course, the students are required to complete four projects. If there

are ten different projects to choose from, how many ways can a student choose the

four projects

i) if there are no restrictions? ii)if two of the projects are compulsory for all students?

i) In a sewing kit, there are 4 bundles of thread of different colors, 8 needles, 5 white

buttons and 9 black buttons. In how many ways one can choose one of the bundles of

thread, one of the needles, one of the white buttons and one of the black buttons.

j) A dinner set at Marvellous Barbeque Restaurant provides the following choices:

Appetizer: Soup or Salad

Entree: Chicken, Beef Brisket, Ribs, or Sausage

Dessert: Apple Pie or Choclate Cake

How many different meals can be served up at this restaurant?

Question 9

i)

Richard has 5 pairs of black trousers, 3 pairs of blue trousers, 4 white shirts, 2 black shirts and 3 blue shirts in his cupboard. Everyday, he selects a pair of trousersand a shirt at random.

1. Find the values of a, b and c indicated on the tree diagram.

1. Calculate the probability that Richard

1. will wear the blue trousers.
2. will wear a black shirt.
3. will NOT wear a pair of blue trousers and a white shirt.
4. will select a pair of trousers and a shirt of the same colour.
5. will wear theblack trousers if he will select a pair of trousers and a shirt of the same colour.

ii)A sample of 500 respondents was selected in a large metropolitan area to study consumer behavior. Among the questions asked was “Do you enjoy shopping for clothing?” Of 230 males (M), 126 answered yes (Y). Of 270 females (F), 36 answered no (N).

a)Evaluate the,,,, and.

b) What is the probability that a respondent chosen at random is a female or enjoys

shopping for clothing?

iii) A box contains one yellow, two white and four brown marbles. Two marbles are selected in succession without replacement at random.

Let V ={Both marbles selected are different in color}

W ={At least one of the marble is white}

a)Find . b) Find .

c) Prove that events V and W are not mutually exclusive.

Question 10

i) A study on the relationship between smoking and lung canceris carried out with 500 people. Following is the result of the study:

If a person is selected at random, find the probability that the person

a)does not have lung cancer.

b)is a nonsmoker given that he/she has lung cancer.

c)is a nonsmoker but he/she has lung cancer.

d)Are events ‘lung cancer’ and ‘smoker’statistically independent? Explain your answer.

ii)

There are a total of 100 go-karts used in a karting driving and training centre. The table below represents the tabulation of the go-karts according to its models and performances.

a) If a go-kart is selected at random, find the probability that the go-kart is in high performance (H), given that it is a Go-kart A model.

b) Are events ‘Go-kart B’ model and ‘Low (L)’ performance independent? Explain your answer.

iii) If 5 products are picked at random from a shelf at a supermarket containing 5 cans of

tuna, 10 cans of sardine and 15 cans of baked beans,

a)in how many ways can the product be chosen if there are no restrictions?

b)what is the probability that 3 cans of tuna and 2 cans of baked beans are selected?

c)what is the probability that at least 4 cans of sardine are selected?

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