KING ABDULAZIZ UNIVERSITY FACULTY OF ENGINEERING Mark ... · In a medical study, patients are...

KING ABDULAZIZ UNIVERSITY

FACULTY OF ENGINEERING

DEPARTMENT OF INDUSTRIAL ENGINEERING

Submittion Date: ….…/…..…/……, Time: …… ….…

HW # Chapters Exercises

1 1 2

Not in Textbook

(4, 8, 50), 5, 14, 16, 22, 33, (32, 43), (41,

47), 51, 56, 60, 75, 80, 92, (96, 98)

Name

ID No.

Section FA GA NG1 DAG XBG IC

01 02 03 04 05 06

Instructor Eng. Mohammed Alharkan Dr. Safa Elaskary

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Spring 2014/2015

Mark

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36

Text Book: “Probability & Statistics for Engineers and Scientists”, Walpole, R., Myers,R., Myers, S. and Ye, K. 9th

Ed., 2012, Pearson.

IE255; HW#1 1 out of 9

Q1.1. The following data represent the length of life, in years, of 50 batteries manufactured by a certain company:

4.2 1.0 2.1 3.2 3.6 1.9 3.8 2.1 1.8 1.2

1.1 0.0 3.6 4.2 0.8 0.4 1.7 1.1 4.2 2.2

1.5 0.8 4.7 2.5 2.5 3.7 2.0 1.2 2.4 1.5

4.7 3.9 2.9 1.9 2.0 3.8 2.4 4.0 3.0 1.6

1.7 3.6 1.3 3.3 2.0 0.6 4.0 3.0 2.0 1.0

a. Calculate the mean, mediam , mode, 10% trimmed mean, variance, standard deviation and range for this set of data.

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b. Construct a stem and leaf plot.

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Chapter 1


c. Set up a relative frequency distribution.

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e. Construct a relative frequency histogram and estimate the frequency distribution.

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f. Comment on the skewness.

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g. Draw a box plot and find the outliers (if any).

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Q2.1. (based on Problem 2.4, 2.8 & 2.50; page 42) An experiment involves tossing two dice, one red and one white, and recording the number that come up. If x equals the outcome on the red die and y equals the outcome on the white die. a. Describe the sample space by using the rule method. b. Let A be the event that the sum of the two dice is greater than 7. B be the event that 3 occurs on either die or both. C be the event that a number greater than 4 comes up on the red die. List the elements corresponding to the events: A, B, C, A C, B A, and B’ C. c. Construct a Venn Diagram to illustrate the intersection and unions of the events A, B, and C. d. Assume that the dice are fair. Find the probability of A, B’, C, B A.

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Chapter 2


Q2.2. (based on Problem 2.5; page 42) An experiment consists of tossing a die and then flipping a coin if the number on the die is even. If the number on the die is odd, the coin is flipping twice. Construct a tree diagram to show the 18 elements of the sample space with the corresponding probability of each element.

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Q2.3. (based on Problem 2.14; page 43) If S = {0, 1, 2, 3, 4, 5, 6, 7} and A = {0, 2, 4, 6}, B = {1, 3, 5, 7}, C = {2, 4, 5}, and D = {1, 7}, list the elements of the sets corresponding to the following events: a. C’; b. (C‘ ∩ D) B; c. (S ∩ A)’; d. A ∩ C ∩ D’.

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Q2.4. (based on Problem 2.16; page 43) If S = {x | 0 < x < 14}, M = {x | 2 < x < 9}, and N = {x | 1 < x < 11}, find: a. M N; b. M’ ∩ N.

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Q2.5. (based on Problem 2.22; page 51) In a medical study, patients are classified in 8 ways according to their blood type and also according to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified according to both blood type and blood pressure.

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Q2.6. (based on Problem 2.33; page 52) If a multiple-choice test consists of 6 questions, each with 4 possible answers of which only 1 is correct, a. in how many different ways can a student check off one answer to each question? b. in how many ways can a student check off one answer to each question and get all the answers wrong?

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Q2.7. (based on Problem 2.32 & 2.43; page 52) a. In how many ways can 8 people be lined up to get on a bus? b. In how many ways can 8 different trees be planted in a circle?

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Q2.8. (based on Problem 2.41 & 2.47; page 52) a. Find the number of ways that 8 teachers can be assigned to 3 different sections of an introductory

statistics course if no teacher is assigned to more than one section. b. How many ways are there to select 3 candidates from 8 equally qualified recent graduates for jobs

in an accounting firm?

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Q2.9. (based on Problem 2.51; page 59) A box contains 600 envelopes, of which 125 contain $100 in cash, 195 contain $25, and 280 contain $10. An envelope may be purchased for $25. What is the sample space for the different amounts of money? Assign probabilities to the sample points and then find the probability that the first envelope purchased contains less than $100.

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Q2.10. (based on Problem 2.56; page 60) An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is a probability of 0.28 of a defect in the brake system, 0.16 of a defect in the transmission, 0.21 of a defect in the fuel system, and 0.35 of a defect in some other area. a. What is the probability that the defect is the brakes or the fueling system if the probability of

defects in both systems simultaneously is 0.14? b. What is the probability that there are no defects in either the brakes or the fueling system?

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Q2.11. (based on Problem 2.60; page 60) In a high school graduating class of 120 students, 58 studied mathematics, 77 studied physics, and 38 studied both mathematics and physics. If one of these students is selected at random, find the probability that: a. the student took mathematics or physics; b. the student did not take either of these subjects; c. the student took physics but not mathematics.

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Q2.12. (based on Problem 2.75; page 69) A random sample of 250 adults is classified below by sex and their level of education attained.

Education Male Female

Elementary 48 44

Secondary 38 60

College 33 27

If a person is picked at random from this group, find the probability that: a. the person is a male, given that the person has a secondary education; b. the person does not have a college degree, given that the person is a female.

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Q2.13. (based on Problem 2.80; page 70) The probability that an automobile being filled with gasoline also needs an oil change is 0.28; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and the filter need changing is 0.16. a. If the oil has to be changed, what is the probability that a new oil filter is needed? b. If a new oil filter is needed, what is the probability that the oil has to be changed?

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Q2.14. (based on Problem 2.92; page 71) Suppose the diagram of an electrical system is as given as follow: What is the probability that the system works? Assume the components fail independently.

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0.6

0.9

0.7

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Q2.15. (based on Problem 2.96 & 2.98; page 77) Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 30%, 25%, 30%, and 40% of the time. If a person who is speeding on his way to work all the times has probabilities of 0.3, 0.2, 0.3, and 0.2, respectively, of passing through these locations. a. What is the probability that he will receive a speeding ticket? b. If this person received a speeding ticket on his way to work, what is the probability that he passed

through the radar trap located at L3?

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KING ABDULAZIZ UNIVERSITY FACULTY OF ENGINEERING Mark ... · In a medical study, patients are...

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