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Econ 2083
Dr. Saleheen Khan
Spring 2011
Home assignment #3
1.
Given that z is a standard normal random variable, compute the following probabilities.
a.
P(1 ≤ z ≤ 0)
b.
P(1.5 ≤ z ≤ 0)
c.
P(2
z
0)
˂ ˂
d.
P(2.5 ≤ z ≤ 0)
e.
P(3
z
≤0)
˂
2.
Given that z is standard normal random variables, find z for each situation.
a.
The area between 0 and z is .4750
b.
The area between 0 and z is .2291
c.
The area to the right of z is .1314
d.
The area to the left of z is .6700
3.
Given that z is a standard normal random variables, find z for each situation
a.
The area to the left of z is .2119
b.
The area between –z and z is .9030
c.
The area between –z and z is .2052
d.
The area to the left of z is .9948
e.
The area to the right of z is .6915
4.
The average American male adult is 5 feet 9 inches tall (Astounding Averages, 1995) .
Assume the standard deviation is 3 inches in answering the following questions.
a.
What is the probability an adult male is taller than 6 feet
b.
What is the probability an adult male is shorter than 5 feet?
c.
What is the probability an adult male is between 5 feet 6 inches and 5 feet 10 inches?
d.
What is the probability an adult male is no more than 6 feet tall?
5.
Trading volume on the New York Stock Exchange has been growing in recent years. For
the first two weeks of January 1998, the average daily volume was 646 million shares
(Barron’s, January 1998). The probability distribution of daily volume is approximately
normal with a standard deviation of about 100 million shares.
a.
What is the probability trading volume will be less than 400 million shares?
b.
What percentage of the time does the trading volume exceed 800 million shares?
c.
If the exchange wants to issue a press release on the top 5% of trading days,
what
volume will trigger a release?
6.
The average age for a person getting married for the first time is 26 years (U>S News &
World Report, June 6, 1994). Assume the ages for the first marriages have a normal
distribution with a standard deviation of four years.
a.
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 Spring '11
 Khan

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