Download Economics 302 Quiz #1

Economics 302
Professor Meyer
Quiz #2
Fall 1999
Name: _______________________________
1.
A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of
minor defect that will require a slight adjustment. (12 points)
a. What is the appropriate probability distribution for the number of defective frames in a random sample of 20 frames?
Defend your answer.
The appropriate probability distribution is a binomial distribution with n=20 and p=.05. You can view the outcome as a series
of independent Bernoulli trials, each of which have an identical probability of success (.05). The number of successes is
distributed as a binomial random variable.
b.
What is the probability that in a sample of 20 window frames, none will need adjustment?
P(X=0) = .3585
c.
What is the probability that in a sample of 20 window frames, more than 2 will need adjustment?
P(X>2) = 1-P(X2) = 1-.9245 = .0755
2.
Assume that Z is a standard normal random variable. (12 points)
a. What is the probability that Z is less than –1.4?
P(Z<-1.4) = .5 – P(0<Z<1.4) = .5 - .4192 = .0808
b.
What is the probability that Z is between 0.42 and 0.90?
P(.42<Z<.90) = P(0<Z<.90) – P(0<Z<.42) = .3159-.1628 = .1531
c.
What is the probability that Z is exactly equal to 1?
The probability that a continuous random variable takes on any particular value is zero.
3.
A recent study of the hourly wages of maintenance crews for major airlines showed that the wages were normally
distributed with a mean of $16.50 and a standard deviation of $3.50. (14 points)
a. If we select a crew member at random, what is the probability that the crew member earns between $16.50 and
$20.00 per hour?
P(16.50<X<20) = P(0<Z<1) = .3413
b.
If we select a crew member at random, what is the probability that the crew member earns more than $20.00 per
hour?
P(Z>1) = .5 - P(0<Z<1) = .5 - .3413 = .1587
4.
Assume you are interested in studying municipal government spending in Alabama. According to the Statistical Abstract
of the United States, there are 434 municipal governments in the state. (12 points)
a. How would you choose a systematic sample of 10 municipalities?
Using a random number table, choose a starting value between 1 and 47. Then, from a list of all the governments (in random
order), starting with the value from the random number table, choose every 43 rd government on the list. This will give
you a sample of 10 governments.
b.
How would you choose a stratified sample of 10 municipalities?
Divide the population into strata based on some characteristic of interest. Population size might be one example. Then, from
within each stratum, choose randomly so that your total sample is equal to 10.