What is the standard deviation of the time

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Reference no: EM131371232

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.


3,138	3,898	4,498	9,443	5,319	9,223
2,366	1,001	3,653	4,895	5,819	3,135
6,201	9,585	5,022	4,322	9,856	4,128

Fill in the frequency table of the final digit of 18 randomly selected phone numbers.

Digit	Frequency
0
1
2
3
4
5
6
7
8
9

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.

Technician	Shutdowns
Taylor	4
Hurley	3
Gupta	5
Rousche	5
Huang	3

(a) How many samples, without replacement, of size two are possible?

Different samples

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?

(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 %

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.)

Sample	Values	Sum	Mean
1	2,2,3
2	2,2,5
3	2,2,6
4	2,3,5
5	2,3,6
6	2,5,6
7	2,3,5
8	2,3,6
9	2,5,6
10	3,5,6

(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.

Number Name		Address	Type
CO	Bethesda North	10500 Montgomery	M/S
		Cincinnati. Ohio 45242
01	Ft. RaniIton-Hughes	630 Eaton Avenue	WS
		Hamilton. Ohio 45013
02	Jevrish Hospital-	4700 East Galbraith Rd.	M/S
	Kern.Mal	Gicinnati, Ohio 45236
03	Mercy Hospital-	3000 Mack Road	M/S
	Fairfield	Fairfield. MN 45014
04	Mercy Hospital-	100 RNerfront Plaza	M/S
	Hamilton	Hamilton. Ohio 45011
05	Middletown	105 Mcibight Drive	M/S
	Regional	Middletown. Ohio 45044
C6	Clermont Mercy	3000 Hospital Dr.	M/S
	Hospital	Batavia, Ohio 45103
07	Mercy Hospital-	7500 State Road	M/S
	Anderson	Citinnati, Ohio 45255
08	Bethesda 0*	619 0* Street	WS
	Hospital	Ciiiiinnati, Ohio 45206
09	Children's Hospital	3333 Banat Avenue	M/S
	Medical Center	Cincinnati, Ohio 45229
10	Christ Hospital	2139 Auburn Avenue	M/S
		Cincinnati, Ohio 45219
11	Deaconess	311 Straight Street	WS
	Hospital	Cincinnati, Ohio 45219
12	Good Samaritan	375 Dixmyth Avenue	WS
	Hospital	Ciyinnati, Ohio 45220
13	Jewish Hospital	3200 Burnt Avenue	M/S
		Cincinnati, Ohio 45229
14	University Hospital	234 Goodman Street	WS
		Cincinnati, Ohio 45267

ID Number Name		Address	Type
15	Providence Hogan!	2446 Kipling AVM*	M/S
		Cincinnati. Ohio 45239
16	St. Francis-	3131 Queen City Avenue	M/S
	St. George Hospital	Cincinnati. Ohio 45238
17	St. Eizabeth Medea]	401 E. 20th Street	WS
	Center, North Unit	CcMngton, Kentucky 41014
18	St. Eizsbeth Medical	One Medical Village	WS
	Center, Sat Unit	Edgewood. Kentucky 41017
19	St. Luke's Hospital	7380 Turfway Dr.	M/S
	West	Florence, Kentucky 41075
20	St. Luke's Hospital	85 North Grand Avenue	M/S
	East	Ft. Thomas. Kentucky 41042
21	Cam Unit Hospital	3156 Cienmore Avenue	S
	Cinb.	Cincinnati, Ohio 45211
22	Emerson Behavioral	2446 Kipling Avenue
	Science	Cincinnati, Ohio 45239
23	Pauline Warfield	1101 Summit Pd.
	Lewis Center for	Cincinnati, Ohio 45237
	Psychiatric Treat.
24	Children's Psychiatric	502 Farrell Drive
	No. Kentucky	Cmington, Kentucky 41011
25	Drake Center Rehab-	151 W. Galbraith Road
	Long Term	Cincinnati, Ohio 45216
26	No. Kentucky Rehab	201 Medical Wage
	Hospital-Short Term	Edgewood. Kentucky
27	Sinners Bums	3229 Burnet Avenue
	Institute	Cincinnati. Ohio 45229
28	VA Medical Center	3200 Vine
		Cincinnati, Ohio 45220

(b) Compute the mean of the population. (Round your answer to 1 decimal place.)

Mean of the population

Reference no: EM131371232

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