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Math 141:Introductory Statistics Question Paper

Math 141:Introductory Statistics

Course:Bachelor Of Science

Institution: Egerton University question papers

Exam Year:2011

INSTRUCTIONS
Answers question one and any other questions:
Question one: (30mks)
1. Explain the difference between the following terms: (4mks)
a)Census and sampling
b)Discrete and continuous sampling
2. Consider the following frequency distribution table:

Class 21-30 31-40 41-50 51-60 61-70
F F f+2 f-3 F+6 F+5

The mean of the data is 47.25, find the value of f. (4mks)
3. If the class marks of the frequency distribution are: 7.265, 7.305, 7.345, 7.385 and 7.425, find the class boundaries and class limits. (3mks)
4. If P(A)=0.3, P(B)=0.4, P(AnB)=0.1
Find (3mks)
a)P(AuB)
b)P(B’/A)
c)P(A’uB)
5 An experiment is repeated 6 times, and the probability of success at each trial is 0.7. Find the probability of (4mks)
a)At most 4 successes
b)2 failures

6. Given below is the frequency distribution of the marks obtained by 90 students.
Marks 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
F 5 12 15 20 18 10 6 4

Calculate the: (9mks)
a)Median
b)80th percentile
c)9th Decile
7. A bag contains five white, three red and two blue balls. If three balls are selected at random , what is the probability that they are:
a)All white
b)All different colours
Question two: (20mks)
1. The following table shows the length of 40 leaves:
Length(mm) 118-126 127-135 136-144 145-153 154-162 163-171 172-180
Frequency 3 5 9 12 5 4 2

a)Draw a histogram ( 3mks)
b)Calculate the mode ( 3mks)
c)Calculate mean absolute deviation, MAD and Quartile deviation,QD. (10mks)

2. The results for some ungrouped frequency distribution of positive observations given as ?¦f_i =60
and ?¦?f_i x_i^2 ?=875.Determine the mean given that variance is? s?^2=2095/708
(4mks)

Question three: (20mks)
1. Given that P(A)=0.7 and P(A?B)=0.8 find P(B)
a)If A and B are mutually exclusive
b)If A and B are independent
c)If P(A/B)=0.6 (5mks)

2. Sixty percent of students in a school are boys. Eight percent of the boys and seventy five percent of the girls have tickets for a school activity. A ticket is found and turned into the school “lost and found department.” What is the probability that it belongs to a girl? (5mks)
3. There are three economist, 4 engineers,2 statisticians and 1 doctor. A committee of 4 from them is to be formed. Find the probability that the committee
Consists of one of each profession
a)Has at least one economist
b)Have the doctor as a member and three others.
(7mks)

Question four: (20mks)
1. The probability that a fisherman has successful day’s fishing is 0.6. Given that he fishes for six days every week, find the probability that in any week he has
a)Exactly four successful days,
b)At least two successful days,
c)At most two successful days,
(7mks)
2. The distribution of marks obtained by a group of students may be assumed to be normal with mean 50 marks and standard deviation 15 marks.
a)Estimate the proportion ( probability) of students with marks below 35
b)The proportion of students with marks between 65 and 80 marks
c)If 20% of the students secured more than k marks, determine k
(7mks)
3. It is proposed that to convert a set of values of a variable X, whose mean and standard deviation are 20 and 5 respectively, to a set of values of a variable Y whose mean and standard deviation are 42 and 8 respectively. If the conversion formula is Y=aX+b, calculate the values of a and of b. ( 6mks)

Question five: (20mks)
1. Twelve people of different ages were given a memory test with the following results:
Age X: 70 68 62 53 50 46 35 28 25 22 20 18
Test Score Y: 48 50 60 55 62 74 69 78 82 80 93 90

a)Find the correlation coefficient between X and Y. (5mks)
b)Compute a linear regression line of Y on X. (6mks)
c)Estimate the test score of a person whose age is 35. ( 2mks)
2. A problem in statistics is given to three students A, B and C whose chances of solving it are ½, ¼ and ½ respectively. What is the probability that the problem will be solved? (3mks)

3. Given that the mean and standard deviation of a set of values are 10 and 2 respectively, write down the new values of the mean and the standard deviation when

a)Each value is increased by a constant 5,
b)Each value is multiplied by a constant 10.
(4mks)

Math 141:Introductory Statistics Question Paper

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