MAT 2170 Exam #3 Review Sheet 2016

HARDMAN
MAT
2170
Exam
#3 Review Sheet

1. Know the definitions of the following terms:

Census

Standard Error

Uniform Continuous Distribution

Statistic

Sample

Normal Distribution

Point Estimator

Sampling Distribution

Parameter

Central Limit Theorem

Z-number

Sampling Frame

Simple Random Sample

Stratified Random Sampling
Cluster Sampling

Systematic Sampling

Convenience Sampling

Judgment Sampling

2. The mean hourly pay rate
for financial managers in the East North Central region is $32.62, and the standard
deviation is $2.32. Assume that pay rates are normally distributed. What hourly
rate separates the top 5% of pay rates from the lower 95% of pay rates for
these financial managers?

3. Each sample statistic on
the left is used as a point estimator of one of the population parameters on the right. Match them up
correctly. Each letter is used once, or not at all.

____ .gif”> A. .gif”>
B. .gif”>
____ .gif”> C. .gif”>
D. .gif”>
____ .gif”> E. .gif”>

4. A recent survey of MBA
graduates revealed that their mean salary was $95,000, with a standard deviation of $12,000. If a simple random sample of 50 MBA graduates
is to be taken:

a. What is the probability that the sample mean salary will exceed
$98,000?

b. What is the probability that the sample mean salary will fall between
$92,000 and $96,500?

5. Given that z is the
standard normal random variable, find z for each situation:

a. The area to the right of z is 0.1314.

b. The area between.gif”>z and z is 0.903.

6. A population has a mean of
200 and a standard deviation of 50. A simple random sample of size 100 will be taken and the sample mean will be
used to estimate the population
mean. Specify the sampling distribution
of.gif”>.

7. If the population
proportion is 0.4, and a simple random sample of size 200 will be taken:

a. Specify the sampling distribution of.gif”>, the sample proportion.

b. What is the probability that the sample proportion will take a value
between 0.36 and
0.42?

8. Given that z is the
standard normal random variable, sketch the appropriate figure that accompanies each probability
(complete with the appropriate shading to represent the probability), and compute the following probabilities:

a. .gif”>

b. .gif”>

c. .gif”>

9. The label on a bottle of
salad dressing shows the contents to be 16 ounces per bottle. The production operation fills the bottles
uniformly according to the following probability
density function:

.gif”>

a. Sketch a graph of the pdf.

b. What is the probability that the bottle will be filled with
between 15.9 and 16.1 ounces?

c. Calculate the probability that a randomly chosen bottle will be
filled with exactly
16 ounces.

d. Quality control accepts a bottle that is filled to within 0.03
ounces of the number of
ounces shown on the label. What is the probability that a bottle of this salad dressing will
fail to meet the quality control standard?