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Introduction To Probability Theory Question Paper

Introduction To Probability Theory

Course:Bachelor Of Science In Applied Statistics

Institution: Maseno University question papers

Exam Year:2012

MASENO UNIVERSITY
SCHOOL OF MATHEMATICS,STATISTICS AND ACTURIAL SCIENCE
SAS 103:Introduction to Probability Theory
C.A.T 2 27th March 2012.
Time:1 hour
Instructions:Answer all Questions

1)Give the probability density function of the normal distribution and state the properties of the distribution.(4 marks)

2)State at least four cases where the normal distribution is not applicable. (2 marks)

3)Molly earned a score of 940 on a national achievement test.The mean test score was 850 with a standard deviation of 100.What proportion of the students had a higher score than Molly?(assume that the test scores are normally distributed)(4 marks)
4)Consider families with three children.Suppose that the proportion of girls in the whole population is 0.488.Assume that the outcome of each birth in the family is independent of the previous outcomes.
a.Define an appropriate random variable concerning the birth outcomes in the family.
(2 marks)
b.State the distribution that the above random variable follows.Justify your answer.
(2 marks)
c.Calculate the probability that there will be
i.less than two girls
ii.exactly three boys (6 marks)
5)Bob is a high school basketball player.He is a 70% free throw shooter.That means his probability of making a free throw is 0.70.During the season,what is the probability that Bob makes his third free throw on his fifth shot?
What distribution have you used in your calculation?
State its properties.(10 marks)

Introduction To Probability Theory Question Paper

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