Chap 7 exercises - Statistics for Business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Môn: Statistics for Business (BAO8OIU)

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Profile Mai Nguyệt
INTERNATIONAL UNIVERSITY Semester 1, Academic Year 2018-2019
STATISTICS FOR BUSSINESS TA NGUYEN BAO MINH TRI –
1
TUTORIAL MATERIAL
Continuous Random Variables
1. Electronic Device Parking Motorbike takes averagely 160 microseconds to respond to motorbike license
plate; with the standard deviation is 30 microseconds. The Device is Normally Distributed. What is the
probability that a device will respond within 100 to 180 microseconds?
2. The time, in hours, that a copying machine may work without breaking down is a normally distributed
random variable with mean 549 and standard deviation 68. Find the probability that the machine will work fo
at least 500 hours without breaking down?
3. The yield, in tons of ore per day, at a given coal mine is approximately normally distributed with mean 785
tons and standard deviation 60.
a. Find the probability that at least 800 tons of ore will be mined on a given day.
b. Find the proportion of working days in which anywhere from 750 to 850 tons is mined.
c. Find the probability that on a given day, the yield will be below 665 tons.
4. Scores on a management aptitude examination are believed to be normally distributed with mean 650 (out o
total of 800 possible points) and standard deviation 50.
a. What is the probability that a randomly chosen manager will achieve a score above 700?
b. What is the probability that the score will be below 750?
5. The price of a share of Kraft stock is normally distributed with mean 33.30 and standard deviation 6.10
a. What is the probability that on a randomly chosen day in the period for which our assumptions are made
the price of the stock will be more than $40 per share?
b. Less than $30 per share?
6. The power generated by a solar electric generator is normally distributed with mean 15.6 kilowatts and
standard deviation of 4.1 kilowatts. We may be 95% sure that the generator will deliver at least how many
kilowatts?
7. Short-term rates fluctuate daily. It may be assumed that the yield for 90-day Treasury bills in early 2007 was
approximately normally distributed with mean 4.92% and standard deviation 0.3%. Find a value such that
95% of the time during that period the yield of 90-day T-bills was below this value.
8. The number of people responding to a mailed information brochure on cruises of the Royal Viking Line
through an agency in San Francisco is approximately normally distributed. The agency found that 10% of th
time, over 1,000 people respond immediately after a mailing, and 60% of the time, at least 650 people
respond right after the mailing. Find the mean and the standard deviation of the number of people who
respond following a mailing.
9. The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean
of 115 mg with a standard deviation of 20 mg.
a. What is the probability that a randomly chosen cup of home-brewed coffee will have more than 130 mg
of caffeine?
b. Less than 100 mg?
c. A very strong cup of tea has a caffeine content of 91 mg. What is the probability that a cup of coffee will
have less caffeine than a very strong cup of tea?
10. The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 579 MP
with a standard deviation of 14 MPa.
a. What is the probability that a randomly chosen sample of glass will break at less than 579 MPa?
b. More than 590 MPa?
c. Less than 600 MPa?
INTERNATIONAL UNIVERSITY Semester 1, Academic Year 2018-2019
STATISTICS FOR BUSSINESS TA NGUYEN BAO MINH TRI –
2
11. The length of a certain kind of Colorado brook trout is normally distributed with a mean of 12.5 inches and a
standard deviation of 1.2 inches. What minimum size limit should the Department of Natural Resources set
it wishes to allow people to keep 80 percent of the trout they catch?
12. Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 28
minutes and a standard deviation of 4 minutes, while method B has a mean of 32 minutes and a standard
deviation of 2 minutes.
a. Which procedure is preferred if the procedure must be completed within 28 minutes?
b. Thirty-eight minutes?
c. Thirty-six minutes?
13. In Santa Theresa, false alarms are received at the downtown fire station at a mean rate of 0.3 per day.
a. What is the probability that more than 7 days will pass before the next false alarm arrives?
b. Less than 2 days?
14. Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders p
hour. Find the probability that:
a. at least 30 minutes will elapse before the next telephone order
b. less than 15 minutes will elapse
c. between 15 and 30 minutes will elapse.
15. At a certain Noodles & Company restaurant, customers arrive during the lunch hour at a rate of 2.8 per
minute. What is the probability that:
a. at least 30 seconds will pass before the next customer walks in
b. no more than 15 seconds
c. more than 1 minute
16. The time it takes a ski patroller to respond to an accident call has an exponential distribution with an averag
equal to 5 minutes.
a. In what time will 90 percent of all ski accident calls be responded to?
b. If the ski patrol would like to be able to respond to 90 percent of the accident calls within 10 minutes,
what does the average response time need to be?
17. Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders p
hour.
a. Find the median waiting time until the next telephone order.
b. Find the upper quartile of waiting time before the next telephone order.
c. What is the upper 10 percent of waiting time until the next telephone order?
18. The mean life of a certain computer hard disk in continual use is 8 years.
a. How long a warranty should be offered if the vendor wants to ensure that not more than 10 percent of th
hard disks will fail within the warranty period?
b. Not more than 20 percent?
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INTERNATIONAL UNIVERSITY
Semester 1, Academic Year 2018-2019 TUTORIAL MATERIAL Continuous Random Variables
1. Electronic Device Parking Motorbike takes averagely 160 microseconds to respond to motorbike license
plate; with the standard deviation is 30 microseconds. The Device is Normal y Distributed. What is the
probability that a device wil respond within 100 to 180 microseconds?
2. The time, in hours, that a copying machine may work without breaking down is a normal y distributed
random variable with mean 549 and standard deviation 68. Find the probability that the machine wil work fo
at least 500 hours without breaking down?
3. The yield, in tons of ore per day, at a given coal mine is approximately normal y distributed with mean 785
tons and standard deviation 60.
a. Find the probability that at least 800 tons of ore wil be mined on a given day.
b. Find the proportion of working days in which anywhere from 750 to 850 tons is mined.
c. Find the probability that on a given day, the yield wil be below 665 tons.
4. Scores on a management aptitude examination are believed to be normal y distributed with mean 650 (out o
total of 800 possible points) and standard deviation 50.
a. What is the probability that a randomly chosen manager wil achieve a score above 700?
b. What is the probability that the score wil be below 750?
5. The price of a share of Kraft stock is normal y distributed with mean 33.30 and standard deviation 6.10
a. What is the probability that on a randomly chosen day in the period for which our assumptions are made
the price of the stock wil be more than $40 per share? b. Less than $30 per share?
6. The power generated by a solar electric generator is normal y distributed with mean 15.6 kilowatts and
standard deviation of 4.1 kilowatts. We may be 95% sure that the generator wil deliver at least how many kilowatts?
7. Short-term rates fluctuate daily. It may be assumed that the yield for 90-day Treasury bil s in early 2007 was
approximately normal y distributed with mean 4.92% and standard deviation 0.3%. Find a value such that
95% of the time during that period the yield of 90-day T-bil s was below this value.
8. The number of people responding to a mailed information brochure on cruises of the Royal Viking Line
through an agency in San Francisco is approximately normal y distributed. The agency found that 10% of th
time, over 1,000 people respond immediately after a mailing, and 60% of the time, at least 650 people
respond right after the mailing. Find the mean and the standard deviation of the number of people who respond fol owing a mailing.
9. The caffeine content of a cup of home-brewed coffee is a normal y distributed random variable with a mean
of 115 mg with a standard deviation of 20 mg.
a. What is the probability that a randomly chosen cup of home-brewed coffee wil have more than 130 mg of caffeine? b. Less than 100 mg?
c. A very strong cup of tea has a caffeine content of 91 mg. What is the probability that a cup of coffee wil
have less caffeine than a very strong cup of tea?
10. The fracture strength of a certain type of manufactured glass is normal y distributed with a mean of 579 MP
with a standard deviation of 14 MPa.
a. What is the probability that a randomly chosen sample of glass wil break at less than 579 MPa? b. More than 590 MPa? c. Less than 600 MPa?
STATISTICS FOR BUSSINESS – TA NGUYEN BAO MINH TRI 1 INTERNATIONAL UNIVERSITY
Semester 1, Academic Year 2018-2019
11. The length of a certain kind of Colorado brook trout is normal y distributed with a mean of 12.5 inches and a
standard deviation of 1.2 inches. What minimum size limit should the Department of Natural Resources set
it wishes to al ow people to keep 80 percent of the trout they catch?
12. Times for a surgical procedure are normal y distributed. There are two methods. Method A has a mean of 28
minutes and a standard deviation of 4 minutes, while method B has a mean of 32 minutes and a standard deviation of 2 minutes.
a. Which procedure is preferred if the procedure must be completed within 28 minutes? b. Thirty-eight minutes? c. Thirty-six minutes?
13. In Santa Theresa, false alarms are received at the downtown fire station at a mean rate of 0.3 per day.
a. What is the probability that more than 7 days wil pass before the next false alarm arrives? b. Less than 2 days?
14. Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders p
hour. Find the probability that:
a. at least 30 minutes wil elapse before the next telephone order
b. less than 15 minutes wil elapse
c. between 15 and 30 minutes wil elapse.
15. At a certain Noodles & Company restaurant, customers arrive during the lunch hour at a rate of 2.8 per
minute. What is the probability that:
a. at least 30 seconds wil pass before the next customer walks in b. no more than 15 seconds c. more than 1 minute
16. The time it takes a ski patrol er to respond to an accident cal has an exponential distribution with an averag equal to 5 minutes.
a. In what time wil 90 percent of al ski accident cal s be responded to?
b. If the ski patrol would like to be able to respond to 90 percent of the accident cal s within 10 minutes,
what does the average response time need to be?
17. Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders p hour.
a. Find the median waiting time until the next telephone order.
b. Find the upper quartile of waiting time before the next telephone order.
c. What is the upper 10 percent of waiting time until the next telephone order?
18. The mean life of a certain computer hard disk in continual use is 8 years.
a. How long a warranty should be offered if the vendor wants to ensure that not more than 10 percent of th
hard disks wil fail within the warranty period? b. Not more than 20 percent?
STATISTICS FOR BUSSINESS – TA NGUYEN BAO MINH TRI 2