1. Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 90 seconds to 13 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.
(a) What are the values for a and b in minutes? (Do not round your intermediate calculations. Round your answer to 1 decimal place.)
(b1) What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)
(b2) What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)
(c) What percent of the problems take more than 5 minutes to resolve? (Do not round your intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)
(d) Suppose we wish to find the middle 50 percent of the problem-solving times. What are the end points of these two times? (Do not round your intermediate calculations. Round your answers to 3 decimal places.)
2. Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 38.5 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.2 minutes.
(a) What percent of the New York City commutes are for less than 26 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)
(b) What percent are between 26 and 34 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)
(c) What percent are between 26 and 45 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.)
3. The Bureau of Labor Statistics' American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged .15 hour (9 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.0 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends:
(a) Less than 8 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.)
4. List the major characteristics of a normal probability distribution. (Select all that apply.)
Skewed.
Symmetrical.
Bell-shaped.
Asymptotic family of curves.
Uniform.
5. A population consists of the following five values: 11, 13, 15, 17, and 21.
(a) List all samples of size 3, and compute the mean of each sample. (Round your Mean value to 2 decimal places.)
(b) Compute the mean of the distribution of sample means and the population mean. (Round your answers to 2 decimal places.)
6. Given below are the last four digits of 18 random phone numbers of your local population.
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3,138
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3,898
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4,498
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9,443
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5,319
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9,223
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2,366
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1,001
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3,653
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4,895
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5,819
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3,135
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6,201
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9,585
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5,022
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4,322
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9,856
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4,128
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Fill in the frequency table of the final digit of 18 randomly selected phone numbers.
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Digit
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Frequency
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0
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1
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2
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3
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4
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5
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6
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7
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8
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9
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Using the sample mean of the final four digits (9704 would lead to a mean of 5), compute the mean of the sample means. (Round your answer to 2 decimal places.)
Mean of the sample means
7. In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.60 hours per week playing organized sports. The population's standard deviation is 2.00 hours per week. Based on a sample of 49 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.
(a) Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)
(b) What is the chance HLI will find a sample mean between 5 and 6.2 hours? (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)
(c) Calculate the probability that the sample mean will be between 5.4 and 5.8 hours. (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)
(d) How strange would it be to obtain a sample mean greater than 7.90 hours?
8. The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.
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Technician
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Shutdowns
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Taylor
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4
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Hurley
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3
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Gupta
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5
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Rousche
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5
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Huang
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3
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(a) How many samples, without replacement, of size two are possible?
Different samples
(c) Compute the mean of the sample means and compare it to the population mean. (Round your answers to 1 decimal place.)
The mean of the sample means is
The population mean is
Both means are
9. Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,100 per hour and a standard deviation of $285.
What is the operating cost for the lowest 3 percent of the airplanes?
10. The cost per item at a supermarket follows an exponential distribution. There are many inexpensive items and a few relatively expensive ones. The mean cost per item is $6.00. What is the percentage of items that cost:
(a) Less than $3.00? (Round your answer to 4 decimal places.)
11. A uniform distribution is defined over the interval from 6 to 10.
(a) What are the values for a and b?
(b) What is the mean of this uniform distribution?
(c) What is the standard deviation? (Round your answer to 2 decimal places.)
(d) The total area is 1.00.
(e) Find the probability of a value more than 7. (Round your answer to 2 decimal places.)
(f) Find the probability of a value between 7 and 9. (Round your answer to 1 decimal place.)
12. The mean of a normal probability distribution is 60; the standard deviation is 5.
(a) About what percent of the observations lie between 55 and 65?
Percentage of observations %
(b) About what percent of the observations lie between 50 and 70?
Percentage of observations %
(c) About what percent of the observations lie between 45 and 75?
Percentage of observations %
13. The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $50,000 per year. Rachel works in the retail industry, where the mean salary for executives with less than 5 years' experience is $35,000 with a standard deviation of $8,000. Rob is an engineer. The mean salary for engineers with less than 5 years' experience is $60,000 with a standard deviation of $5,000.
(1) Compute the z values for both Rob and Rachel. (Round your answers to 3 decimal places. Negative amount should be indicated by a minus sign.)
(2) Comment on your findings.
Adjusting for their industries, Rob is well average and Rachel well .
14. A population consists of the following five values: 2, 2, 3, 5, 6.
(a) List all samples of size 3, and compute the mean of each sample. (Round sample means to 2 decimal places.)
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Sample
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Values
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Sum
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Mean
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1
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2,2,3
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2
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2,2,5
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3
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2,2,6
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4
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2,3,5
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5
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2,3,6
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6
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2,5,6
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7
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2,3,5
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8
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2,3,6
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9
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2,5,6
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10
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3,5,6
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(c) Compute the mean of the distribution of sample means and the population mean.(Round your answers to 1 decimal place.)
15. The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,175 per month and a standard deviation of $250 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed.
What is the probability of selecting a sample of 70 one-bedroom apartments and finding the mean to be at least $2,115 per month? (Round z value to 2 decimal places and final answer to 4 decimal places.)
16. The following is a list of hospitals in the Cincinnati (Ohio) and Northern Kentucky Region. Also included is whether the hospital is a general medical/surgical hospital (M/S) or a specialty hospital (S). We are interested in estimating the average number of full- and part-time nurses employed in the area hospitals.
(a) A sample of five hospitals is to be randomly selected. The random numbers are 09, 16, 00, 49, 54, 12, and 04. Which hospitals are included in the sample? Use ID numbers to identify the hospitals. (Select hospital names included in sample in numerical order.)
(c) A sample is to consist of every fifth location. We select 02 as the starting point. Which hospitals will be included in the sample? (Hint: Enter the ID number used to identify the hospitals)
17. Scrapper Elevator Company has 20 sales representatives who sell their product throughout the United States and Canada. The number of units sold by each representative is listed below. Assume these sales figures to be the population values.
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Number Name
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Address
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Type
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CO
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Bethesda North
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10500 Montgomery
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M/S
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Cincinnati. Ohio 45242
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01
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Ft. RaniIton-Hughes
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630 Eaton Avenue
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WS
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Hamilton. Ohio 45013
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02
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Jevrish Hospital-
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4700 East Galbraith Rd.
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M/S
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Kern.Mal
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Gicinnati, Ohio 45236
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03
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Mercy Hospital-
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3000 Mack Road
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M/S
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Fairfield
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Fairfield. MN 45014
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04
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Mercy Hospital-
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100 RNerfront Plaza
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M/S
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Hamilton
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Hamilton. Ohio 45011
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05
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Middletown
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105 Mcibight Drive
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M/S
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Regional
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Middletown. Ohio 45044
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C6
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Clermont Mercy
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3000 Hospital Dr.
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M/S
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Hospital
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Batavia, Ohio 45103
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07
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Mercy Hospital-
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7500 State Road
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M/S
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Anderson
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Citinnati, Ohio 45255
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08
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Bethesda 0*
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619 0* Street
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WS
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Hospital
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Ciiiiinnati, Ohio 45206
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09
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Children's Hospital
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3333 Banat Avenue
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M/S
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Medical Center
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Cincinnati, Ohio 45229
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10
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Christ Hospital
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2139 Auburn Avenue
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M/S
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Cincinnati, Ohio 45219
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11
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Deaconess
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311 Straight Street
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WS
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Hospital
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Cincinnati, Ohio 45219
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12
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Good Samaritan
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375 Dixmyth Avenue
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WS
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Hospital
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Ciyinnati, Ohio 45220
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13
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Jewish Hospital
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3200 Burnt Avenue
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M/S
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Cincinnati, Ohio 45229
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14
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University Hospital
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234 Goodman Street
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WS
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Cincinnati, Ohio 45267
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ID
Number Name
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Address
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Type
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15
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Providence Hogan!
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2446 Kipling AVM*
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M/S
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Cincinnati. Ohio 45239
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16
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St. Francis-
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3131 Queen City Avenue
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M/S
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St. George Hospital
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Cincinnati. Ohio 45238
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17
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St. Eizabeth Medea]
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401 E. 20th Street
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WS
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Center, North Unit
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CcMngton, Kentucky 41014
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18
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St. Eizsbeth Medical
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One Medical Village
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WS
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Center, Sat Unit
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Edgewood. Kentucky 41017
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19
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St. Luke's Hospital
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7380 Turfway Dr.
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M/S
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West
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Florence, Kentucky 41075
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20
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St. Luke's Hospital
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85 North Grand Avenue
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M/S
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East
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Ft. Thomas. Kentucky 41042
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21
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Cam Unit Hospital
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3156 Cienmore Avenue
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S
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Cinb.
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Cincinnati, Ohio 45211
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22
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Emerson Behavioral
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2446 Kipling Avenue
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Science
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Cincinnati, Ohio 45239
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23
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Pauline Warfield
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1101 Summit Pd.
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Lewis Center for
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Cincinnati, Ohio 45237
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Psychiatric Treat.
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24
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Children's Psychiatric
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502 Farrell Drive
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No. Kentucky
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Cmington, Kentucky 41011
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25
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Drake Center Rehab-
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151 W. Galbraith Road
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Long Term
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Cincinnati, Ohio 45216
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26
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No. Kentucky Rehab
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201 Medical Wage
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Hospital-Short Term
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Edgewood. Kentucky
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|
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27
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Sinners Bums
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3229 Burnet Avenue
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Institute
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Cincinnati. Ohio 45229
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|
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28
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VA Medical Center
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3200 Vine
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|
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Cincinnati, Ohio 45220
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|
(b) Compute the mean of the population. (Round your answer to 1 decimal place.)
Mean of the population