1. The following values represent the population of home mortgage interest rates (in percents) being charged by the banks in a particular city:
| 6.9 |
7.5 |
6.5 |
7 |
7.3 |
6.8 |
6.5 |
| 7 |
7 |
7.2 |
7.5 |
7.8 |
6 |
7 |
Given this information, what is the most extreme amount of sampling error possible if a random sample of n = 4 banks is surveyed and the mean loan rate is calculated?
2. Beacon Hill Trees & Shrubs currently has an inventory of 10 fruit trees, 8 pine trees, and 14 maple trees. It plans to give 4 trees away at next Saturday's lawn and garden show in the city park. The 4 winners can select which type of tree they want. Assume they select randomly.
What is the probability that no fruit trees and 2 of each of the others will be selected? 23)
3. Harrison Water Sports has three retail outlets: Seattle, Portland, and Phoenix. The Seattle store does 50 percent of the total sales in a year, while the Portland store does 35 percent of the total sales. Further analysis indicates that of the sales in Seattle 20 percent are in boat accessories. The percentage of boat accessories at the Portland store is 30 and the percentage at the Phoenix store is 25. If a sales dollar is recorded as a boat accessory, the probability that the sale was made at the Portland store is
4. The URS construction company has submitted two bids, one to build a large hotel in London and the other to build a commercial office building in New York City. The company believes it has a 40% chance of winning the hotel bid and a 25% chance of winning the office building bid. The company also believes that winning the hotel bid is independent of winning the office building bid.
What is the probability the company will win at least one contract?
5. The file CEO Compensation contains data on the annual salaries of the CEO's of several major US companies. Use this data to find the mean, the median, and the interquartile range for CEO compensation. Finally, construct a histogram for the salaries, using 12 bins of equal width (for simplicity, round bin width up to the nearest million dollars).
The histogram is worth 3 points. The mean, median, and interquartile range are worth one point each.
6. It is thought that the time between customer arrivals at a fast food business is exponentially distributed with λ equal to 5 customers per hour. Given this information, what is the mean time between arrivals? Round your answer to the nearest minute, if necessary.
7. The Jack In The Box franchise in Bangor, Maine, has determined that the chance a customer will order a soft drink is 0.90. The probability that a customer will order a hamburger is 0.60. The probability that a customer will order french fries is 0.50.
The restaurant has also determined that if a customer orders a hamburger, the probability the customer will also order fries is 0.80.
Determine the probability that the order will include a hamburger and fries.
8. The makers of Sweet-Things candy sell their candy by the box. Based on company policy, the mean target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy. In order to do this, with a mean weight of 2 pounds, what must the standard deviation be? Assume that the box weights are normally distributed, and round your answer to two decimal places if necessary.
9. Dell Computers receives large shipments of microprocessors from Intel Corp. It must try to ensure the proportion of microprocessors that are defective is small. Suppose Dell decides to test five microprocessors out of a shipment of thousands of these microprocessors. Suppose that if at least one of the microprocessors is defective, the shipment is returned.
If Intel Corp.'s shipment contains 10% defective microprocessors, calculate the probability the entire shipment will be returned. Round your answer to three decimal places.
10. The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour What are the chances that no customers will arrive in a 15-minute period? (Round your answer to three decimal places if necessary)
11. The probability function for random variable X is specified as:
f(X)=X/6 for X = 1,2 or 3
Determine the expected value of X.
12. The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $36.25 and a standard deviation equal to $80. Based on this information, what are the chances that the revenue on the first show will be between $300 and $500?
13. Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes.
What is the probability that more than four customers will arrive in a 30-minute segment? Round your answer to three decimals.
14. If the number of defective items selected at random from a parts inventory is considered to follow a binomial distribution with n = 50 and p = 0.10, the standard deviation of the number of defective parts is (round your answer to two decimal places if necessary):
15. It is assumed that the time customers spend in a record store is uniformly distributed between 3 and 12 minutes. Based on this information, what is the probability that a customer will spend more than 9 minutes in the record store?
16. A company that makes chocolate chip cookies has found that the number of chips per cookie follows a Poisson distribution. What should the minimum average number of chips be so that 99 percent or more of the cookies have at least one chocolate chip? Find the minimum average to nearest whole chip (i.e. choose an average that is a whole number).
17. The weight of sacks of potatoes is normally distributed with a mean of 20 pounds and a standard deviation of 2 pounds. The weight of sacks of onions is also normally distributed with a mean of 20 pounds and a standard deviation of 0.50 pounds. Based on this information, which product will yield the highest probability of getting a very heavy sack?
18. A random variable, x, has a normal distribution with μ = 13.6 and σ = 2.90. Determine a value, x(), so that P(μ - xo ≤ x ≤ μ + xo) = 0.95. Round your answer to three decimal place
19. The time between calls to an emergency 911-call center is exponentially distributed with a mean time between calls of 645 seconds. Based on this information, what is the probability that the time between the next two calls is between 200 and 400 seconds? Round your answer to two decimal places.
20. Assume that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more?
21. You only need to do ONE of the following two problems. If you correctly solve both, you will get extra credit.
A claim was recently made on national television that two of every three doctors recommend a particular pain killer. Suppose a random sample of n = 300 doctors revealed that 180 said that they would recommend the painkiller. If the TV claim is correct, what is the probability of 180 or fewer in the sample agreeing?
22. The St. Joe Company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of 0.5 inch. A random sample of n = 50 trees is collected. What is the probability of the sample mean being less than 2.9 inches?
Attachment:- Data.xlsx