Name:______ID:______

Treatment of Experimental Data 85-222 Winter 2005

Faculty of Engineering

University of Windsor

Midterm Exam I Solution

Friday, February 11, 11:30 am – 1:30 pm, Ambassador Auditorium

Instructor: Mohammed Fazle Baki

Aids Permitted: Calculator, straightedge, and text (no notes).

Time available: 2 hour

Instructions:

  • This solution has 9 pages.
  • Please be sure to put your name and student ID on each odd-numbered page.
  • State answers upto four decimal places.
  • Show your work.

Grading:

QuestionMarks:

1/10

2/7

3/9

4/5

5/8

6/5

7/4

8/8

9/9

Total:/65

Question 1: (10 points) Circle the most appropriate answer

1.1Descriptive statistics involves data

  1. collection
  2. organizing or summarizing
  3. presentation
  4. all of the above

1.2Nominal data

  1. allow all arithmetic operations
  2. convey ranking
  3. represents arbitrary codes
  4. represents quantity or amounts of something such as length, weight, etc.

1.3Which of the following is an advantage of sampling?

  1. Accuracy of information
  2. Cost of data collection
  3. Both
  4. None

1.4A bar chart

  1. emphasizes trend, if any
  2. emphasizes relative values e.g., frequencies
  3. can show order of categories
  4. b and c

1.5The following is the most suitable measure of central tendency for ranked data

  1. Mean
  2. Median
  3. Mode
  4. b and c

1.6Defining sample variance as the mean squared deviation from the sample mean tends to

  1. Underestimate the population variance
  2. Overestimate the population variance
  3. Accurately estimate the population variance
  4. b and c

1.7For positively skewed data

  1. mean > median
  2. mean = median
  3. mean < median
  4. there are usually two modes

1.8If A and B are two mutually exclusive events

  1. P(A)+P(B)=1
  2. P(A and B) = P(A)×P(B)
  3. P(A or B) = P(A)+P(B)
  4. P(A|B) = P(A)

1.9The reliability increases

  1. if the components are in parallel and the number of components increases
  2. if the components are in series and the number of components increases
  3. if the components are in parallel and the number of components decreases
  4. b and c

1.10An example of a continuous random variable is the one that assumes value of

  1. number of defective parts in a production lot
  2. time between two customers arriving in a bank
  3. number of accidents per month
  4. b and c

Question 2: (7 points) Descriptive statistics

A major airline wanted some information on those enrolled in their “frequent flyer” program. A sample of 20 members resulted in the following number of miles flown, to the nearest 1000 miles, by each participant.

21 / 19 / 23 / 22 / 20 / 19 / 17 / 22 / 14 / 20
19 / 11 / 16 / 16 / 13 / 18 / 12 / 15 / 23 / 24
  1. (2 points) Construct a frequency distribution table for the data, using five class intervals and the value 10 as the lower limit for the first class.
  1. (4 points) Construct a relative frequency histogram for the data, using five class intervals and the value 10 as the lower limit for the first class.
  1. (1 point) Comment if the data is symmetric, positively skewed, or negatively skewed. Justify your answer in brief.

The data is negatively skewed. The mean is less than the median. There are more larger numbers than smaller numbers.

Question 3: (9 points) Central location and box plot

The following are numbers of twists that were required to break 11 forged alloy bars: 24, 39, 48, 26, 35, 38, 54, 23, 34, 29, and 37. Find:

  1. (1 point) Mean

=35.1818

  1. (2 point) The 30th percentile

First, sort the data: 23, 24, 26, 29, 34, 35, 37, 38, 39, 48, 54

  1. (3 points) The first, second and third quartiles.

The 1st quartile:

The 2ndquartile:

The 3rdquartile:

  1. (3 points) Construct a box plot.

Question 4: (5 points) Variation

A. A. Michelson (1852-1931) made many series of measurements of the speed of light. Using a revolving mirror technique, he obtained

12, 30, 30, 27, 30, 39, 18, 27, 48, 24, 18

for the differences (velocity of light in air) – (299,700) km/s. Find:

  1. (1 point) Range

Range = Largest value – smallest value = 48 –12 = 36

  1. (3 points) Variance

Marking note: The sample variance must be computed for experimental data. It’s incorrect to compute population variance. 1 point is taken off if denominator shows instead of

  1. (1 point) Standard deviation

Question 5: (8 points) Probability laws

Consider the following information about 500 machine parts which are inspected before shipping:

The machine part is improperly assembled
(A) / The machine part is properly assembled
(AC) / Total
The machine part contains one or more defective components
(D) / 10 / 5 / 15
The machine part contains no defective component
(DC) / 20 / 465 / 485
Total / 30 / 470 / 500

Find:

  1. (2 points)
  1. (2 points)
  1. (2 points)

Alternately,

Marking note: Since, there are some cases (10) when the events and occur simultaneously, the events are not mutually exclusive. If addition law is used to solve the problem, the general addition law must be used. It’s incorrect to use the addition for mutually exclusive events. So, 1 point is taken off for missing.

  1. (2 points)

Alternately,

Question 6: (5 points) Probability trees

The Olive Construction Co. is determining whether it should submit a bid for the construction of a new shopping center. In the past, Olive’s main competitor, Base Construction Co., has submitted bids 60% of the time. If Base Construction Co. does not bid on a job, the probability that the Olive Construction Co. will get the job is 0.80; if Base Construction Co. does bid on a job, the probability that the Olive Construction Co. will get the job is 0.25.

  1. (4 points) Construct a probability tree showing all the probabilities, simple events and joint probabilities.

Define the following events:

: Base construction bids on the job

: Olive Construction gets the job

  1. (1 point) What is the probability that the Olive Construction Co. will get the job?

Question 7: (4 points) Reliability

Compute the reliability of the following system:

Question 8: (8 points) Expected value and variance

Let Xbe a random variable with the following probability distribution:

x / -10 / -5 / 0 / 5 / 10
p(x) / 0.10 / 0.15 / 0.25 0.20 / 0.30 / 0.25

Compute

  1. (2 points) E(X)
  1. (2 points) Var(X)

Var(X)

Alternately, Var(X) =

Var(X) =

  1. (1 point) E(3X+2)
  1. (1 point) Var(3X+2)

Var(3X+2) =

  1. (2 points) E(3X2+4)

Alternately,


Question 9: (9 points) Binomial distribution

A study of 5-year trends in the logistics information systems of industries found that the greatest computerization advances were in transportation (Industrial Engineering, July 1990). Currently, 40% of all industries contain shipping open order files in their computerized data base. In a random sample of 10 industries, let equal the number that include shipping open order files in their computerized data base. Note that the probability distribution of can be modelled using the binomial distribution. Find:

  1. (3 points) using Binomial distribution formula
  1. (3 points) using Binomial distribution formula
  1. (1 point) using Binomial distribution table

= 0.9877 from Table A, Appendinx A

  1. (1 point) using Binomial distribution table
  1. (1 point) using Binomial distribution table

1