STA 1202(F)/Page 1 of 6

INTI INTERNATIONAL UNIVERSITY

FOUNDATION IN BUSINESS INFORMATION TECHNOLOGY (CFPI)/

FOUNDATION IN SCIENCE (CFSI)

STA1202: STATISTICS

FINAL EXAMINATION: SEPTEMBER 2012 SESSION

Instructions: This paper consists of SIX (6) questions. Answer any FIVE (5) questions in the

answer booklet provided. All questions carry equal marks.

Question 1

( a ) Two events are such that 891.0)( AP and 109.0)( BP . Find )( BAP if

( i ) event A and B are mutually exclusive.

(2 marks)

( ii ) event A and B are exhaustive.

(2 marks)

( iii ) event A and B are independent.

(2 marks)

( b ) The weights of Christmas cards posted by Miss-Soong-Baby are normally distributed

with mean 20g. It is found that the weights of 94% of the cards are within 12g of the

mean.

( i ) Find the standard deviation of the weights weigh of the cards.

(3 marks)

( ii ) Find the probability that a randomly chosen card weighs more than 13g.

(2 marks)

( iii ) Find the probability that a randomly chosen card weighs between 8g and 32g.

(3 marks)

( c ) The daily demand for a Star Newspaper in a bookshop has a Poisson distribution

with mean 3.8 . Find the probability that in a day there are exactly fifty copies

requested.

(2 marks)

( d ) A biased die was thrown 20 times and the number of time a number 5 is observed was

noted. This experiment was repeated many times and the average number of times a

number 5 was observed was found to be 4.8. Find the probability that in the next 20

throws the number of times a number 5 is observed will be less than three.

(4 marks)

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Question 2

( a ) The discrete random variable X has the following probability distribution. The mean of X

is 1.05.

X 2 1 0 1 2 3

)( xXP 0.08 p 0.12 0.16 q 0.22

( i ) Write down two equations involving p and q and hence find the values of p and

q .

(4 marks)

( ii ) Calculate ),(XVar

(2 marks)

( iii ) Find )(XVarXP . (2 marks)

( b ) Miss Soong-Baby selects toast for breakfast with a probability of 0.85. If she selects toast

then the probability that she will have peanut jam on it is 0.8. If she has a bread roll then

the probability that she will have peanut jam on it is 0.4.

( i ) Draw a tree diagram showing all the possible outcomes and their probabilities.

(2 marks)

( ii ) Find the probability that Miss Soong-Baby did not have peanut jam for breakfast.

(2 marks)

( iii ) Given that Miss Soong-Baby did not have peanut jam for breakfast, find the

probability that she had toast.

(2 marks)

( c ) A bag contains 10 Mashimaro of which 7 are green and 3 are white. A Mashimaro is

picked at random from the bag and its colour is noted. The Mashimaro is not replaced. A

second Mashimaro is then picked. Find the probability that

( i ) the first Mashimaro is green.

(2 marks)

( ii ) the first Mashimaro is green and the second Mashimaro is white.

(2 marks)

( iii ) the Mashimaro are of different colours.

(2 marks)

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Question 3

( a ) The data below shows the graduate lists grade for 56 students in May 2012 from south area states (Malacca, Selangor, Negeri Sembilan and Johor).

GS GS GS DL GS GS GS GS GS GS GS DL

GS GS GS GS GS GS GS GS GS DL GS GS

GS GS GS DL GS GS GS GS GS GS GS GS

GS GS GS DL GS GS GS GS GS PL GS DL

GS GS GS GS DL GS DL

( i ) Copy and complete the table below. (3 marks)

Grade Number of students

Presidents List (PL)

Deans List (DL)

Good Standing (GS)

( ii ) Using a scale of 2 cm to 5 students on the horizontal axis and 2 cm to 1 grade on

the vertical axis, draw a bar chat to represent the distribution. (3 marks)

( b ) A Tesco shopping complex has the three types of staff. One person from the shopping

complex is chosen at random.

Gender Female Male

Administrative 34 41

Managerial 12 30

Operational 45 38

( i ) What is the probability that the person is a female? (2 marks)

( ii ) What is the probability that the person is a male operator? (2 marks)

( iii ) What is the probability that the person is either an operator or an administrator?

(2 marks)

( iv ) Given that an administrative staff is selected, what is the probability that the staff

is a male? (2 marks)

( c ) )35.0,15(~ BinX , Find

( i ) ).(XE

(2 marks)

( ii ) ).(XVar

(2 marks)

( iii ) .3XP (2 marks)

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Question 4

( a ) The table shows the distribution of the height of 40 plants of star-fruit trees which have

been planted in Miss Soong-Babys garden for 5 weeks.

Height (cm) 4-5 6-7 8-9 10-11 12-13 14-15

Frequency 2 8 14 11 4 1

( i ) Copy and complete the table below.

Height

(cm)

Frequency Cumulative

Frequency

Mid-point x

fx 2fx

4 5 2

6 7 8

8 9 14

10 11 11

12 13 4

14 15 1

fx 2fx

(6 marks)

( ii ) Find the mean of the data.

(2 marks)

( iii ) Find the mode of the data using formula.

(2 marks)

( iv ) Find the median of the data using formula.

(2 marks)

( v ) Find the standard deviation of the data using formula.

(2 marks)

( b ) The random variable X has a normal distribution with mean 4.5. It is given that

0465.05.5 XP (see diagram). Give the answer in four decimal points.

( i ) Find the standard deviation of X. (3 marks)

( ii ) Find the probability that a random observation of X lies between 3.8 and 4.8.

(3 marks)

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Question 5

( a ) The table shows the amount of milk (measured to the nearest litre) produced by 54 cows

in a farm in Kedah per day. Draw a histogram to show the information below.

(4 marks)

( b ) The random variable 210,60~ NX . Find

( i ) 62XP , (2 marks)

( ii ) 75XP . (2 marks)

( c ) The histogram shows the number of patients treated at a clinic in Malacca everyday

during a certain period of time.

( i ) Copy and complete the table below. (8 marks)

Class Interval Frequency Mid-point x fx 2fx 39.5 49.5

49.5 59.5

59.5 69.5

f fx 2fx

( ii ) Find the mean of the data. (2 marks)

( iii ) Find the variance of the data using formula. (2 marks)

Amount of milk, l (litre) Number of cows

155 x 16

2015 x 11

2520 x 6

3525 x 21

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Question 6

( a ) X is a random variable with Poisson probability distribution. Find

( i ) 2XP when = 3. (2 marks)

( ii ) 52 XP when = 4. (2 marks)

( b ) Given that X is a discrete random variable with the probability distribution below.

X 1 2 3 4

)( xXP 0.2 0.1 0.4 0.3

( i ) Find )(XE .

(2 marks)

( ii ) Find )(XVar .

(2 marks)

( c ) The transmission on a model of a Toyota Car has a warranty of 40,000 miles. It is known

that the life of such a transmission has a normal distribution with mean of 72,000 miles

and a variance of 144,000,000 miles2. Find the probability of the transmission that

( i ) will fail before the warranty period.

(3 marks)

( ii ) will be good for more than 100,000 miles.

(3 marks)

( d ) A fair die is tossed 6 times. Find the probability that

( i ) the number 1 is obtained exactly 4 times,

(2 marks)

( ii ) the number 2 is obtained at least once,

(2 marks)

( iii ) the number 2 is obtained at most 1 time.

(2 marks)

--THE END-- STA1202(F)/SEP2012/SCJ/031012