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Tutorial 4
Business statistics (Đại học Kinh tế Quốc dân)
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NATIONAL ECONOMICS UNIVERSITY
ADVANCED EDUCATIONAL PROGRAM
BUSINESS STATISTICS
Tutorial 4
This tutorial will demonstrate some of the concepts we have discussed in the lectures about
probability distributions of both discrete and continuous variables.
Question 1
Write down the sample space of rolling a pair of dice (one white dice and one black dice).
Calculate:
(a) The probability of getting at least one double six in 24 throws of this experiment.
(b)The probability of the event A that the faces sum up to 3.
Now we throw the white dice before the black dice and suppose that the white dice comes up 1
(c)What is the probability of A?
Question 2
Sketch the distribution of Z, a standard normal variable. Use printed tables to answer the
following.
(d)Find the probabilities listed below.
i. P(Z<1.07)
ii. P(Z>-1.21)
iii. P(-1.32<Z<1.99)
(e)Find the value of c which makes the following statements
true. i. P(Z<c)=0.20
ii. P(|Z|>c)=0.02
iii. P(|Z|<c)=0.90
Question 3
Z. Inc., in the Sweden has developed a new product. The demand for the new product is
uncertain but can be described as ‘high’ or ‘low’ in any one year. After 4 years, the product is
expected to be obsolete. Management must decide whether to build a plant or to contract with a
factory in Vietnam to manufacture the product. Building a plant will be profitable if demand
remains high but could lead to a loss if demand drops in future years. After carefull study of the
market and of all relevant costs, Z’s planning office provides the following information. Let A be
the event that the first year’s demand is high, and B the event that the following 3 years’ demand
is high. The marketing division’s best estimate of the probabilities is:
P(A) = 0.9
P(B|A) = 0.36
P(B|Ac) = 0
1
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The probability that building a plant is more profitable than contracting the production to
Vietnam is 0.95 if demand is high all 4 years, 0.3 if demand is high only in the first year, and 0.1
if demand is low all 4 years. Draw a tree diagram that organizes this information. The tree will
have three stages: first year’s demand, next three years’ demand, and whether building or
contracting is more profitable. Which decision has the higher probability of being more
profitable?
Question 4
A fast food chain pays its teenage employees an average wage of $9.20 per hour with a standard
deviation of 50 cents. Assuming wages are approximately normally distributed, answer the
following questions.
(a)What proportion of teenage employees receives wages between $8.50 and $10 per hour?
(b)Nineteen-year-olds, who constitute 6% of the chain’s teenage workforce are the most
highly paid. What would be their minimum hourly wage?
Question 5
A portfolio is composed of two stocks. Given the following parameters associated with the
returns of the two stocks:
Stock
Proportion of portfolio
Mean
Standard Deviation
1
0.30
0.12
0.02
2
0.70
0.25
0.15
a. Determine the mean and standard deviation of the return on the portfolio when
the coefficient of correlation is equal to 0.5; 0.25; and 0.
b. Describe what happens to the expected value and standard deviation of the portfolio
returns when the coefficient of correlation decreases.
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Hints: you need to read an example required in the lecture notes before solving question 4.
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