FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL...

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FACULTY OF APPLIED SCIENCE AND ENGINEERING

FINAL EXAMINATION

MSE238H1S

ENGINEERING STATISTICS

THURSDAY FEBRUARY 26th, 2009

From 3:10 PM to 4:40 PM

Examiner: Professor Stavros A. Argyropoulos

Write Using Capitals

First Name Surname

Student Number Signature

Marks Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8

Total

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ANSWER ALL EIGHT PROBLEMS One aid sheet and non-programmable calculators permitted

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Problem 1 (Marks 12 ) If A and B are independent events, show that A’(i.e. Compliment of A) and B are also independent.

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Problem 2 (Marks 12 ) A factory uses three production lines to manufacture cans of a certain type. The table below gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period.

Type of nonconformance Line 1 Line 2 Line 3

Blemish 15 12 20 Crack 50 44 40

Pull-Tab Problem 21 28 24 Surface Defect 10 8 15

Other 4 8 2

During this period, line 1 produced 500 nonconforming cans,line 2 produced 400 such cans, and line 3 was responsible for 600 nonconforming cans. Suppose that one of these 1500 cans is randomly selected.

a) What is the probability that the can was produced by line 1 ? That the reason of nonconformance is a crack ?

b) If the selected can came from line 1,what is the probability that it had a blemish ? c) Given that the selected can had a surface defect, what is the probability that it

came from line 1 ?

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Problem 3 (Marks 10 ) Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 60% can be repaired, whereas the other 40% must be replaced with new units. If a company purchases ten of these telephones ,what is the probability that exactly two will end up being replaced under warranty ? Hint: Binomial distribution will be applicable here.

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Problem 4 (Marks 12 ) A reservation service employs five information operators. Those information operators receive requests for information independently of one another,each according to a Poisson process with rate λ = 2 per minute.

a) What is the probability that during a given 1-min period,the first operator receives no requests ?

b) What is the probability that during a given 1-min period, exactly four of the five operators receive no requests ?

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Problem 5 (Marks 16 )

The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with α = 25 and b = 35.

a) Determine the probability density function of X b) What is the probability that preparation time exceeds 33 min ? c) What is the probability that preparation time is within 2 min of the mean time ? d) For any such κ that 25< κ < κ +2 < 35 what is the probability that the

preparation time is between κ and κ +2 min ?

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A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. A bearing is acceptable if its diameter is within 0.004 in of its target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with mean value 0.499 in and standard deviation 0.002 in. What percentage of the bearings produced will not be acceptable ?

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The life in hours of a 100-watt light bulb is known to be normally distributed with σ = 20 hours. A random sample of 25 bulbs has a mean value of 1020x = hours.

a) Construct a 95 % two-sided confidence interval on the mean life b) Construct a 95 % lower-confidence bound on the mean life.

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Problem 8 (Marks 14 ) A manufacturer is interested in the output voltage of a power supply used in PC. Output voltage is assumed to be normally distributed, with standard deviation 0.2 Volts, and the manufacturer wishes to test H0: µ = 5 Volts against H1: µ ≠ 5 Volts, using n = 10 units a) Considering the acceptance region as 4.80 5.20x≤ ≤ find the value of α b) Find the power of the test for detecting a true mean output voltage 5.1 Volts

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FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL...

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