**14-1**

List the assumptions that are made in Markov analysis.

**14-7**

Find the inverse of each of the following matrices:

(a) [ 0.9 0.1 ]

[ -0.2 0.7 ]

(b) [ 0.8 -0.1 ]

[ -0.3 0.9 ]

(c) [ -0.2 0.9 ]

[ 0.8 -0.2 ]

(d) [ 0.8 -0.2 ]

[ -0.1 0.7 ]

**14-8**

Ray Cahnman is the proud owner of a 1955 sports car. On any given day, Ray never knows whether his car will start. Ninety Percent of the time it will start if it started the previous morning, and 70% of the time it will not start if did not start the previous morning.

(a) Construct the matrix of transition probabilities.

(b) What is the probability that it will start tomorrow if it started today?

(c) What is the probability that it will start tomorrow if it did not start today?

**14-24**

Set up both the vector of state probabilities and the matrix of transition probabilities given the following information:

Store 1 currently has 40% of the market; store 2 currently has 60% of the market.

In each period, store 1 customers have 80% chance of returning; 20% of switching to store 2.

In each period, store 2 customers have 90% chance of returning; 10% switching to store 1.

**14-25**

Find *TT *(2) for Problem 14-24.

**15-7**

Explain why a process can be out of control even though all samples fall within the upper and lower control limits.

**15-8**

Shader Storage Technologies produces refrigeration units for food producers and retail food establishments. The overall average temperature that these units maintain is 46 degrees Fahrenheit. The average range is 2 degrees Fahrenheit. Samples of 6 are taken to monitor the process. Determine the upper and lower control chart limits for averages and ranges for these refrigeration units.

**15-10**

Zipper Products, INC., produces granola cereal, granola bars, and other natural food products. Its natural granola cereal is sampled to ensure proper weight. Each sample contains eight boxes of cereal. The overall average for the samples is 17 ounces. The range is only 0.5 ounce. Determine the upper and lower control-chart limits for averages for the boxes of cereal.

**15-16**

Colonel Electric is a large company that produces lightbulbs and other electrical products. One particular lightbulb is supposed to have an average life of about 1,000 hours before it burns out. Periodically the company will test 5 of these and measure the average time before these burn out. The following table gives the results of 10 such samples:

(a) What is the overall average of these means? What is the average range?

(b) What are the upper and lower control limits for a 99.7% control chart for the mean?

(c) Does this process appear to be in control? Explain.

**15-17**

For Problem 15-16, develop upper and lower control limits for the range. Do these samples indicate that the process is in control?

Subject | Mathematics |

Due By (Pacific Time) | 01/03/2015 09:00 am |

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