Download Exam2 - Academic Information System (KFUPM AISYS)

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KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICAL SCIENCES
DHAHRAN, SAUDI ARABIA
STAT213 STATISTICS METHODS FOR ACTUARIES
Second Major Exam, Term 112
Time:
6:30 p.m. to 8:00 p.m.,
April 22 , 2012
Instructors: Prof. Hassen Muttlak
Student Surname:
ID#
You are allowed to use electronic calculators and other reasonable writing accessories that help
write the exam. Try to define events, formulate problem and solve. See example below.
Do not keep your mobile with you during the exam, turn off your mobile and leave it aside.
Question No
1
Full Marks
10
2
10
3
15
4
10
Total
45
Marks Obtained
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Q1. [2+3+3+2 =10] Samples of 10 parts from a metal punching process are selected every hour.
Typically, 9% of the parts require rework. Let X denote the number of parts in the sample of 10 that
require rework.
a. What is the probability that X exceeds 1?
b. Find the mean and standard deviation?
c. A process problem is suspected if X exceeds its mean by more than two standard deviations,
what is the probability that X exceeds its mean by more than two standard deviations?
d. If the rework percentage increases to 12%, what is the probability that X less than 2?
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Q2. [2+2+3+3=10]The length of time it takes students to complete an exam is given by a
random variable, Y (measured in hours), which has a probability density function given by:
ky,
f ( y)  
 0,
1 y  4
elsewhere
a. Find the value of k.
b. What is the probability that a student selected by random will finish his exam in less than two
hours and half.
c. Find the mean and the standard deviation of the number of hours that the students
will take to complete this exam.
d. Thirty six students took the exam. What is the probability the sample mean of the
time to complete the exam is less than 3 hours?
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Q3. [2+2+3+5+3=15] Items manufactured at a factory are known to have a normal distribution with
mean length of 100mm and a standard deviation of 3mm.
a. The specifications for this item are that it must have a length of between 90mm and
109mm, what percentage would be within specification?
b. Find the cut off point for the lowest 20% of the specification.
c. A sample of 9 items selected by random, what is the probability that the sample
mean is less than 98mm?
d. In part c suppose that the sample mean of the 9 items is 96, construct a 90%
confidence interval to estimate the population mean and interpret your finding.
e. Suppose that we wish to estimate the population mean to be within 5 marginal
error with 95% confidence level, what is the sample required to insure these
specifications?
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Q4. Answer the following question by choosing the right answer.
1. Which of the following statements are not correct?
a. A discrete random variable X can assume only a finite number of possible values.
b. A discrete random variable X is any random variable whose possible values either
constitutes a finite set or else can be listed in an infinite sequence in which there is a first
element, a second element, and so on.
c. A random variable X is said to be continuous if its set of possible values consists of an entire
interval on the number line.
d. Number of students in your statistics class is an example of a discrete random variable.
2. Which of the following statements is not an example of a discrete random variable?
a. The number of female respondents to a questionnaire about gender differences.
b. The age of female respondents to a questionnaire about gender differences.
c. The number of sales a salesperson makes per year.
d. The number of school-age children is a working woman.
3. Which of the following statements is not an example of a continuous random variable?
a. The weight gain in pounds per month for a calf
b. The price for cheesecake in New York Style cheesecake
c. The time it takes you to finish this statistics test
d. The number of mistakes made by a typist on a randomly chosen page of a physics thesis.
4. Let X be a discrete random variable with var(X) = 8.6, then var(3X + 5.6) is?
a. 77.4
5.
b. 14.2
c. 83.0
d. 31.4
The major difference between the binomial and hypergeometric distributions is that with the
hypergeometric distribution
a. the probability of success must exceed .5
b. the probability of success is not the same from trial to trial
c. the trials are independent of each other
d. the random variable of interest is continuous
e. None of the above statements are true
6. When monitoring the status of a computer system over time, with breakdowns constituting the
events of interest, the appropriate probability distribution is
a. binomial distribution
b. negative binomial distribution
c. Poisson distribution
d. Hypergeometric distribution
7. Unquestionably, the most important and useful distribution in probability and statistics is the?
a.
b.
c.
d.
binomial distribution
normal distribution
gamma distribution
exponential distribution
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8. Which of the following statements are correct?
a. The statement that the random variable X is normally distributed with parameters  and  2 is
often abbreviated X N (  ,  2 ) .
b. If the random variable X is normally distributed with parameters  and  2 , then
E ( X )   and V ( X )   2 .
c. The graph of any normal probability density function is symmetric about the mean and bellshaped, so the center of the bell (point of symmetry) is both the mean of the distribution and
the median.
d. If the random variable X is normally distributed with parameters  and  2 , then a large
 implies that a value of X far from  may well be observed, whereas such a value is quite
unlikely when  is small.
e. All of the above statements are correct
9. Which of the following statements are true?
a. Before the observations in a sample become available, we view each observation as a
random variable.
b. A statistic is a random variable, which will be denoted by an uppercase letter.
c. A lower case letter is used to represent the calculated or observed value of the statistic.
d. None of the above statements is true
e. All of the above statements are true
10. Which of the following statements are correct?
a. The sample mean, regarded as a statistic (before a sample has been selected or an
experiment carried out), is denoted by X while the calculated value of this statistic is x .
b. S 2 represents the sample standard deviation and is regarded as a statistic, while the
calculated value of this statistic is s 2 .
c. A statistic is any quantity whose value can be calculated from population data.
d. All of the above statements are correct
e. None of the above statements is correct