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Probability And Statistics Question Paper
Probability And Statistics
Course:Diploma In Information Technology
Institution: Kca University question papers
Exam Year:2009
UNIVERSITY EXAMINATIONS: 2009/2010
STAGE IV EXAMINATION FOR DIPLOMA IN INFORMATION
TECHNOLOGY
DIT 401: PROBABILITY AND STATISTICS
DATE: NOVEMBER 2009 TIME: 1½HOURS
INSTRUCTIONS: Answer any THREE questions
QUESTION ONE (20 MARKS)
a) Differentiate between the following terms as used in statistics
i). Qualitative and quantitative variables
ii). Descriptive and inferential data (4 Marks)
b) Twenty staff members of a construction company were surveyed to find out what their weekly
wages was in dollars. The results are as follows:
32.7 48.5 48.5 39.1 42.0 28.5 35.5 40.0 40.9 33.2
36.6 42.5 34.5 44.0 39.5 34.2 35.7 32.8 25.4 39.3
i). State whether these data is discrete or continuous, determine the appropriate class interval
and present these data in a grouped frequency distribution table (start with value 25 and use a
class interval of 5) (5 Marks)
ii). Using an appropriate Assumed mean estimate the mean and variance of the data (4 Marks)
c) A coin is tossed twice. Suppose X represents a number of heads that comes up, find the
probability distribution corresponding to the random variable X. (4 Marks)
d) If the mean weekly wage of 86 employees is £172.45 and employee number 87 earned
£158.80. What is the mean wage of all 87 employees? (3 Marks)
2
QUESTION TWO (20 MARKS)
a) Point out the four stages involved in a statistical investigation (2 Marks)
b) The mean of the data below is x.
42, 36, 38, x-25, 51, 38, x, 43
Find,
i). The value of x (2 Marks)
ii). The mean absolute deviation (2 Marks)
iii). The variance of the data (2 Marks)
iv). The lower and upper quartiles (3 Marks)
c) Find the (i) 3rd quartile (ii) 8th deciles and (iii) 50th percentile of the following set of
measurement. (6 Marks)
16 25 4 18 23 13 20 8 11 9 17
d) A fair dice with sides is thrown and a biased coin with P(head) = 2/5 is thrown, find the
probability of getting a tail or a 4 (3 Marks)
QUESTION THREE (20 MARKS)
a) State the four natural forms that can be used to classify data. (4 Marks)
b) The table below shows the marks scored by eight students in two tests; Probability and
Statistics (X), and Programming (Y)
X 67 42 85 51 39 97 81 70
Y 70 59 71 38 55 62 80 76
Calculate Spearman’s coefficient of rank correlation (4 Marks)
c) There are 3 baskets labeled A, B and C. Basket A contains 4 ripe mangoes and 2 unripe ones
and basket B contains 3 ripe mangoes and 2 unripe ones. Basket C contains 2 ripe mangoes and
3 unripe ones. If two mangoes are picked at random from any of the baskets without
replacement,
i). Draw a tree diagram to represent this information and hence, find the probability of
picking (3 Marks)
ii). Two unripe ones (2 Marks)
iii). No ripe ones (2 Marks)
d) The probability that I win a betting game in any one trial is 0.48. Find the probability that I win
seven times in ten independent trials. (3 Marks)
3
e) If the mean of the values 14, y, 17, 16 and y is y+0.4, find the value of y. (2 Marks)
QUESTION FOUR (20 MARKS)
a) From the following frequency distribution
Class 1-10 11-20 21-30 31-40 41-50
Frequency 2 14 22 26 16
Calculate an estimate of the
i).Mean (3 Marks)
ii).Variance and (3 Marks)
iii). Standard deviation (1 Marks)
iv). Find the median hence prove that it is equal to 5th Decile and 50th Percentile
(4 Marks)
b) From the frequency distribution table below
Class 51-59 61-69 71-79 81-89 91-99 101-109 111-119
Frequency 3 5 15 25 20 18 12
i). Draw an OGIVE curve representing given information. (5 Marks)
ii). Using the Assumed mean method calculate the variance (4 Marks)
QUESTION FIVE (20 MARKS)
a) A firm is independently working on two separate jobs. There is a probability of only 0.3
that either of the jobs will be finished on time. Find the probability that
i). Neither job will be finished on time (2 Marks)
ii). At least one job will be finished on time (1 Mark)
b) The table below gives the probability distribution frequency of a random variable X.
X 0 1 2 3
P(x) p 2q p + q q
Given that the mean of X is 1.375, find the values of p and q (6 Marks)
c) Find the modal class and hence calculate the modal wage of the 65 employees whose
distribution is below (5 Marks)
4
Wages 50.00-
59.99
60.00-
69.99
70.00-
79.99
80.00-
89.99
90.00-
99.99
100.00-
109.99
110.00-
119.99
No. of
employees
8 10 16 14 10 5 2
d) Of 8 equal candidates for a job, 3 are qualified accountants, 4 are graduates and 2 have
neither of these qualifications. Find
i).The probability that a graduate gets the job (1 Mark)
ii).Given that a qualified accountant has got the job, the probability that he is a graduate
(3 Marks)
iii).The probability that a qualified accountant gets the job, given that a graduate did not get the
job. (2 Marks)
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