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Sma:160 Introduction To Probability And Statistics Question Paper

Sma:160 Introduction To Probability And Statistics

Course:Bachelor Of Science

Institution: Kenyatta University question papers

Exam Year:2014

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2013/2014
SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE
SMA 160: INTRODUCTION TO PROBABILITY AND STATISTICS
DATE: TUESDAY 1ST APRIL 2014
INSTRUCTIONS
Attempt Question ONE and any other TWO Questions

QUESTION ONE (30 MARKS)
Draw a histogram of the data from the following table (2 marks)
MARKS 0-10 10-20 20-25 25-30 30-40 40-60
FREQUENCY 12 18 10 17 20 23

Obtain the arithmetic mean, median and mode of the following data : (3marks)
X 1 2 3 4 5 6 7
Frequency 5 9 12 17 14 10 6

A sample of the life of refrigerators in years was taken and the results given below:
Life(years) 0-2 2-4 4-6 6-8 8-10 10-12
No of refrigerators 5 16 13 7 5 4

Calculate the mean, median and standard deviation (5 marks)

Three students are selected at random from a statistics class.
List the elements of the sample space using the letter M for male and F for female (1 mark)
Find the probability of selecting one male student (1 mark)
Find the probability of selecting ablest two female students (1 mark)
Find the probability of selecting one female student given that the first student selected is male (1 mark )

The following are the summation of Five observations of the temperature inside a fireplace (F) and the outside temperature (T)
? T=65 ,? F=280,? TF=3782,? T×T=1293 and ? F×F=15756
Determine the linear regression equation of outside temperature and fireplace temperature (5 marks)
Predict the values of the outside temperature when the fireplace temperature is 52? using the equation determined in Q (e) (1) (3 marks)
Compute the co-efficient of correlation between fireplace temperature and outside temperature (3 marks)

Differentiate between Kurtosis and skewness (4 marks)

QUESTION TWO (20 marks)
Consider the following data:
113 106 100 91 100 96 112 107 125 98
105 101 121 101 104 92 101 98 97 110
103 127 94 120 101 93 98 93 93 109
100 91 108 111 95 103 95 118 106 123
102 98 117 98 117 104 98 102 93 105

From the raw data calculate the mean (2 marks)
Construct a frequency distribution table with classes 90-94,95-99 etc (3 marks)
From the distribution obtain:
Mean
Median
Mode
Standard deviation
Coefficient of variation (10 marks)

Sketch a histogram (5 marks )

QUESTION THREE (20 marks)
A manufacturer makes toothpaste. The manufacturer employs an inspector to check the quality of his product. The inspector tested a random sample of the toothpaste from a large
Batch and calculated the probability of any tooth paste packet weight being defective as 0.025. Ms Kapere buys two toothpaste tubes made by the manufacturer. Calculate:
The probability that both pastes are defective (4 marks)
The probability that exactly one of the paste is defective (4 marks)

A university student studying the employment situation in a certain town found out that the probabilities of males and females on employment status is as shown in the table below.

Employed Unemployed
Males 0.40 0.10
Females 0.475 0.025

Suppose an unemployed person is chosen at random. Find the probability that the person selected is:
Male (3 marks)
Female (3 marks)

The probability that a contractor will get a painting contract is 2/3 and the probability that he will not get an electrical contract is 5/9. If the probability of getting at least one contract is 4/5 find the probability that he will get both contracts (6 marks)

QUESTION FOUR (20 MARKS)
Obtain the equation of the two lines of regression for the following data
X: 43 44 46 40 44 42 45 42 38 40 42 57
Y: 29 31 19 18 19 27 27 29 41 30 26 10

For what value of x is y = 49? (13 marks)
A group of eight students obtained the following percentage of marks in a test in statistics and accountancy
Student 1 2 3 4 5 6 7 8
% of marks (statistics) 50 60 65 70 75 40 70 80
% of marks (accountancy) 80 71 60 75 90 82 70 50

Compute the correlation coefficient between statistics and accountancy ( 4 marks)
Compute spearman’s rank correlation coefficient from the above data
(3marks)
QUESTION FIVE (20 marks)
Define µr, the r-th central moment and µr'' the r^Th moment about any point A.
Hence establish the following relations.
µ2= µ^'' 2-(µ^'' 1)^2
µ3=µ^'' 3-3µ^'' 1 µ^'' 2+(µ^'' 1)^3
µ4=µ^'' 4-4µ^'' 1 µ^'' 3+6(µ^'' 1)^2 µ^'' 2-3(µ^'' 1)^4 (7 marks)

The following data are given to an economist for the purpose of economic analysis. The data refer to the length of a certain type of batteries
N=100,? fd=50,? fd^2=1970,? f?d^ ?^3=2948 and ? fd^4=86752 in which d=x-48

Obtain the coefficient of skewness and determine the shape of distribution. Calculate the coefficient of Kurtosis and determine whether the distribution is platykurtic (10 marks)

In a frequency distribution, the coefficient of skewness based on quartiles is 0.6. If the sum of the upper and the lower quartile is 100 and the median is 38,find the value of the upper quartile
(3 marks)

Sma:160 Introduction To Probability And Statistics Question Paper

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