Assignment
1. Match each of the descriptions on the left with the correct lettered terms on the right. Each letter is used once, or not at all.
____ A continuous probability distribution for which the probability that the random variable takes a value in an interval is the same for equal-length intervals.
____ A result that says that may be treated like a normal random variable under certain conditions.
____ A number that describes some trait, or feature, of a population.
____ A data set made up of observations on every element in the population.
____ A probability distribution whose primary defining characteristic is a symmetric, bell-shaped curve.
____ A probability distribution for a sample statistic.
____ A normal random variable minus its mean, divided by its standard deviation.
A. Census
B. Standard Error
C. Uniform
D. Statistic
E. Sample
F. Normal
G. Point Estimator
H. Sampling Distribution
I. Parameter
J. Central Limit Theorem
K. Z-number
2. The mean hourly pay rate for financial managers in the East North Central region is $25.85, and the standard deviation is $5.05. Assume that pay rates are normally distributed. What hourly rate separates the bottom 12% of pay rates from the upper 88% 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.
X‾____ A. p
B. σ
p‾____ C. μ
D. θ
s ____ E. λ
4. A recent survey of MBA graduates revealed that their mean salary was $90,000, with a standard deviation of $9,500. If a simple random sample of 35 MBA graduates is to be taken:
a. What is the probability that the sample mean salary will exceed $92,500?
b. What is the probability that the sample mean salary will fall between $85,000 and $91,500?
5. Given that z is the standard normal random variable, find z for each situation:
a. The area to the left of z is 0.7019.
b. The area between -z and z is 0.8294.
6. A population has a mean of 100 and a standard deviation of 15. A simple random sample of size 50 will be taken and the sample mean will be used to estimate the population mean. Specify the sampling distribution of X‾.
7. If the population proportion is 0.7, and a simple random sample of size 65 will be taken:
a. Specify the sampling distribution of p‾ , the sample proportion.
b. What is the probability that the sample proportion will take a value between 0.65 and 0.83?
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. P[-1.789 < Z ≤ -0.191]
b. P[Z ≥ 1.55]
c. P[-2.07 > Z]
9. A business executive has just been transferred from Chicago to Atlanta and needs to sell her house in Chicago quickly. The executive's employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes that the price she will get by leaving her house on the market for another month is uniformly distributed between $200,000 and $225,000.
a. Sketch the graph of the pdf.
b. If she leaves her house on the market for another month, what is the probability that she will get at least $215,000 for it?
c. If she leaves her house on the market for another month, what is the probability that it will sell for less than $210,000?
d. Should she leave the house on the market for another month, or accept her employer's offer to buy the house now? EXPLAIN YOUR REASONING.