Question 1. Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.' The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 and $15,000.
a. Suppose you bid $12,000. What is the probability that your bid will be accepted?
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
c. What amount should you bid to maximize the probability that you get the property?
d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?
Question 2. For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015 (BusinessWeek, March 20, 2006). Assume the standard deviation is $3540 and that debt amounts are normally distributed.
a. What is the probability that the debt for a borrower with good credit is more than $18,000?
b. What is the probability that the debt for a borrower with good credit is less than $10,000?
c. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?
d. What is the probability that the debt for a borrower with good credit is no more than $14,000?
Question 3. Consider the following exponential probability density function.
f(x) = 1/3 e-x/3 for x ≥ 0
a. Write the formula for P(x ≤ xo).
b. Find P(x ≤ 2).
c. Find P(x ≤ 3).
d. Find P(x ≤ 5).
e. Find P(2 ≤ X ≤ 5).
Question 4. Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 2 can be selected.
a. List the 10 samples beginning with AB, AC, and so on.
b. Using simple random sampling, what is the probability that each sample of size 2 selected?
Question 5. The American Association of Individual Investors (AAII) polls its subscribers on a weekly basis to determine the number who are bullish, bearish, or neutral on the short-term prospects for the stock market. Their findings for the week ending March 2, 2006, are consistent with the following sample results (AM! website, March 7, 2006).
Bullish 409 Neutral 299 Bearish 291
Question 6.
A population has a mean of 200 and a standard deviation of 50. Suppose a simple random sample of size 100 is selected and x' is used to estimate μ.
a. What is the probability that the sample mean will be within ± 5 of the population mean?
b. What is the probability that the sample mean will be within ± 10 of the population mean?
Question 7.
The president of Doerman Distributors, Inc., believes that 30% of the firm's orders come from first-rime customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers.
a. Assume that the president is correct and p = .30. What is the sampling distribution of P' for this study?
b. What is the probability that the sample proportion p' will be between .20 and .40?
c. What is the probability that the sample proportion will be between .25 and .35?