Question 1: Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in "boom" state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a "boom" state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1--and is.
|
State of economy
|
Probability
|
Market Return
|
Gold Return
|
|
Boom
|
0.15
|
25%
|
(-30%)
|
|
Moderate Growth
|
0.35
|
20%
|
(-9%)
|
|
Week Growth
|
0.25
|
5%
|
35%
|
|
No Growth
|
0.25
|
(-14%)
|
50%
|
Based on the expected return, would you rather invest your money in the stock market or in gold? Why?
Question 2: Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Question 3: The average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.3, find the probability that a randomly selected car of this model has a gas mileage between 25.8 and 26.3 miles per gallon.
Question 4: The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28?
Question 5: The normal distribution is:
A. a density function of a discrete random variable
B. a binomial distribution with only one parameter
C. the single most important distribution in statistics
D. a discrete distribution
Question 6: The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:
A. central tendency theorem
B. simple random sample theorem
C. central limit theorem
D. point estimate theorem
Question 7: Mrs. Smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. Assuming that the distribution of words read per minute are normally distributed, what is the minimum number of words per minute a student would have to read in order to get the award?
Question 8: A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. What is the probability of getting a score between 65 and 89 on this exam?
Question 9: Using the standard normal curve, the Z- score representing the 99th percentile is? 95th?
Question 10: If Z is a standard normal variable, then P(Z = 1) = ?