Sma 160: Probabilty And Statistics 1 Question Paper
Sma 160: Probabilty And Statistics 1
Course:Bachelor Of Education Science In Mathematics And Geography
Institution: Kenyatta University question papers
Exam Year:2011
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2010/2011
SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE
SMA 160: PROBABILITY AND STATISTICS 1
DATE: 29th MARCH 2011 TIME: 8.00-10.00AM
INSTRUCTIONS: ANSWER ALL QUESTIONS.
QUESTION 1 [40MARKS]
a) Define the following terms:
i) Statistics
ii) Correlation
b) Differentiate between the following terms:
i) Numerical and categorical data
ii) Skewness and Kurtosis
iii) Independent and mutually exclusive events
c) A box A contains 3 red and 4 green beads and a box B contains 2 red and 5 green beads. Akinyi selects a box and then picks a bead from then box at random. She is twice as likely to choose box B as box A. What is the probability than she selects a green bead?
d) The following incomplete grouped frequency distributions show the weights in kilograms of a population of 100 street girls Nairobi city. Each weight was recorded to the nearest 100 grams.
Weights (kg) Number of girls
10-20
20-30
30-40
40-50
50-60
14
X
27
Y
15
Given that the mode of this distribution is 34, find the values of x and y.
e) Suppose there are two series x11, x12, x13....x1n and 21, x22, x23... x2n. The first series has n1numbers and the second series has n2 numbers. Let the mean of the first series be X and the mean of the second series be X2.Show that X , the mean c of the combined series is given by X=n1 X1+n2 X2/n1+n2
f) The mode and standard deviation of 50 observations are 25 and 6 respectively. Find the coefficient of skewness if the sum of the observations is 900. Comment on your answer.
g) The data relating to the weekly maintenance cost (Y) is $ to the age (X) in months of ten machines of similar type in a manufacturing company was summarized as below.
?X=300, ?Y=2970, ?XY=97650, ?X*2=12050, ?Y*2=913050
Calculate the product moment correlation coefficient between age and cost. Comment on your results
h) Given the set of data: 2,3,7,8 and 10, find the: first, second, third and fourth moments about the mean for this data.
QUESTION 2 (30 MARKS)
a) A car covered 100km at a speed of 60km/h. If an overall speed of 48km/h is to be achieved, at what speed would the car travel on its return journey of 100km?
b) A machine was purchased in 1991. It depreciated at the rate of 8% per annum for the first three years and after that at the rate of 10% per annum for 7 years. Find the average rate of depreciation.
c) The following distribution shows the cumulative frequencies of 230 observations with missing frequencies f1, f2 and f3.If the mode and median are 34 and 33.5 respectively, calculate the missing frequencies.
classes Cumulative frequencies
0-10
10-20
20-30
30-40
40-50
50-60
60-70
4
20
20+f1
20+f1+f2
20+f1+f2+f3
26+f1+f2+f3
30+f1+f2+f3
d) T he following data show marks obtained by 40 students in a statistic test.
99, 72 54 25 40 65 32 60 10 85 48 52 64
74 35 62 51 71 65 57 95 80 56 69 61 45
63 39 73 53 82 76 50 66 60 55 62 75 63
49
Construct a discrete grouped frequency distribution such that each class has a common width of 10 marks and the first class starts with the lowest observation. What percentage of students obtained less than 70 marks?
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