Probability and Statistics (GSDR2109)

Higher Institute of Transport and Logistics (HITL)

Semester: First Semester

Level: 200

Year: 2018

Answers (200 )
School/Faculty: HITL DEPARTMENT: General Studies LECTURER(S): Dr.Nukenine Siri Konje
COURSE CODE: TLGS2109 COURSE TITLE: Probability and Statistics
DATE: 23/03/2018 Duration: 3 hours TIME: 2hr
THE UNIVERSITY OF BAMENDA
P.O BOX 39 Bambili
REPUBLIC OF CAMEROON
Peace-Work-Fatherland
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. 17 0
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Problem 1 (5 points)
Define the following:
(i) A population (ii) A Sample Space (iii) A Sample Random Sample (iv) A Random
Variable
Problem 2 (6 points)
A sample random sample of containers is chosen from a large population of containers in a
certain railway terminal. The heights (in inches) of the containers are given as follows;
30, 223, 232, 223, 75, 80, 80, 126, 105, 138, 149, 179
179, 79, 191, 239, 240, 242, 245, 247, 254, 274, 384, 470
Using the given data, calculate the following;
(i) The sample mean, (ii) The sample median, (iii) The 65
th
percentile of the sample, (iv)
the third Quartile of the sample
Problem 3 (4 points)
A large industrial firm allows discounts on orders (invoices) that are paid within 30 days.
Of all orders, 10% receive a discount. In a company, 12 orders are sampled at random.
What will be the Random variable and how is it distributed? What is the probability that
fewer than 5 of the 12 sampled orders receive the discount?
Problem 4 (8 points)
(a) Suppose that the marks in statics test follow a normal curve, with mean core of 64 and
standard deviation of 3. The statistics marks of three randomly chosen students are 70, 73
and 61. Convert these marks to standard units.
(b) Lifetimes of batteries in a certain application are normally distributed within mean of
50 hours and standard deviation of 5 hours. Find the probability that a randomly chosen
battery will last between 42 and 52 hours.
Problem 5 (12 points)
(a) The sample mean and standard deviation of speeds of 100 vehicles passing a certain
stretch of a Highway is 12.05kmph and 0.1 respectively. Find a 95% and 85%
confidence intervals for the mean speed of the vehicles.
(b) Define the following: (i) Correlation (ii) Correlation confidence (iii) Null
Hypothesis (iv) Alternative Hypothesis
Success Wishes
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