Moana is a sailing from her home to a nearby island which is 215 miles north and 33 miles west. There is a constant ocean current of 0.50 knots moving from west to east. Moana can sail her boat at a cruising speed of 5.5 miles per hour in still water.

1. What angle should Moana sail to get to the island?

2. How long will it take her to get there?

3. Moana’s friend Maui is floating on a raft that is moving with the ocean current (meaning, he is not traveling with respect to the water). Would Maui see Moana’s boat traveling with a speed faster than, slower than, or equal to what an observer standing on the shore would see? Explain your reasoning

Use the data given in the table to answer the following questions. The data represents the average number of miles that a salesperson travels in a day verses the number of sales made each month.

(a) What is the value of the correlation coefficient for this set of data? Round to 3 decimal places.

(b) What is the equation of the Regression Line for this set of data? Round values to two decimal places.

(c) Predict the number of sales an associate could expect to make if he travelled an average of 108 miles each day. Round to two decimal places.

Data are gathered on each car in the motor pool, regarding number of miles (in thousand miles) driven in a given year, and maintenance costs (in thousand dollars) for that year:

Part of the linear regression analysis output are shown in below:

3. Construct a 95% confidence interval for the conditional mean of y given x0=50.

   (A) [2.476, 2.879]   (B) [1.538, 2.409] (C) [1.651, 2.30] (D) [2.410, 2.908]

3. Construct a 95% prediction interval at x0=50.

(A) [2.360, 2.996]

(B) [2.064, 3.254]

(C) [1.612, 2.335]

(D) [2.223, 3.132]

Boston Railroad decided to use the high-low method and operating data from the past six months to estimate the fixed and variable components of transportation costs. The activity base used by Boston Railroad is a measure of railroad operating activity, termed "gross-ton miles," which is the total number of tons multiplied by the miles moved. Transportation Costs Gross-Ton Miles January $530,900 224,000 February 591,900 250,000 March 418,300 162,000 April 567,500 242,000 May 476,000 195,000 June 610,200 263,000 Determine the variable cost per gross-ton mile and the total fixed cost. Variable cost (Round to two decimal places.) $ per gross-ton mile Total fixed cost $

Whenever you are asked to test a hypothesis, be sure to: (a) state the null and alternative hypotheses; (b) state the relevant sample statistic; (c) give the rejection region; (d) compute the test; (e) give your decision and a conclusion in English.

1. Assume that last year, licensed American drivers drove an average of 10,000 miles, with a standard deviation of 2,000 miles (these are population figures). This year, the government campaigned to get people to save gas by driving less. To test the effectiveness of the campaign, a study is conducted. A sample of 100 drivers is drawn at random from the general population and the number o fmiles driven by each person is recorded. On the average, these 100 drivers drove 11,000 miles. Was the campaign effective? Use alpha = .01.

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:

Required:

Use the step method to allocate the service costs, using the following:

The order of allocation starts with Maintenance. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

b. The allocations are made in the reverse order (starting with Cafeteria). (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

Two trains of equal weight, moving with velocities of 30 miles an hour each and in opposite directions collide. Show that the loss of energy caused by the impact is the same as in the case of a train moving at 60 miles an hour striking another at rest. In the latter case, find the velocity with which the debris will be moved along the track. Also show that before impact the total energy in the one case is doubled that in the other

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Tony has had a bad virus and has had to stay in bed for the last ten days. Tony now wants to continue training for that marathon (26 miles) race which will be in one week. He says he has to train by running at least 18 miles a day. What could happen to Tony and what would you advise Tony based on your knowledge of muscles

4.   Sampling and Sampling Distributions

In the most recent hearing on Highway safety at the New York City Council hearings, it was determined that the average travels 1,123 miles per month.  Assume the population standard deviation is 341 miles per month. Determine the interval that will contain 95% of the sample means for the sample size of

a. 30 drivers

b. 45 drivers

c. Explain the difference in these probabilities