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ĐỀ 1
1. The number of pages printed before replacing the cartridge in a laser printer is
normally distributed with a mean of 11,500 pages and a standard deviation of
800 pages. A new cartridge has just been installed.
a.What is the probability that the printer produces more than 12,000 pages before
this cartridge must be replaced?
b.What is the probability that the printer produces fewer than 10,000 pages?
2. In a survey conducted to determine, among other things,the cost of vacations,
64 individuals were randomly sampled.Each person was asked to compute the
cost of her or his most recent vacation.The average cost of the survey is $2000.
Assuming that the standard deviation is $400. estimate with 95% confidence the
average cost of all vacations.
3. The operations manager of a large production plant would like to estimate the
average amount of time workers take to assemble a new electronic component.
After observing a number of workers assembling similar devices,she guesses
that the standard deviation is 6 minutes.How large a sample of workers should
she take if she wishes to estimate the mean assembly time to within 20
seconds?Assume that the confidence level is to be 99%.
4. The Laurier Company's brand has a market share of30%.Suppose that 1,000
consumers of the product are asked in a survey which brand they prefer.What is
the probability that more than 32%of the respondents say they prefer the Laurier brand?
5. A random sample of 18 young adult men(20-30 years old)was sampled.Each
person was asked how many minutes of sports he watched on television daily.The responses are listed here:
50,48,65,74,66,37,45,68,64,65,58,55,52,63,59,57,74,65. It is known that σ=10.Test
to determine at the 5%significance level whether there is enough statistical
evidence to infer that the mean amount of television watched daily by all young
adult men is greater than 50 minutes.
6. A bottling company needs to produce bottles that will hold 12 ounces of liquid
for a local beer maker.Periodically,the company gets complaints that their bottles
are not holding 12 ounces of liquid.The bottling company randomly samples 15
bottles and finds the average amount of liquid held by the 15 bottles is 11.90
ounces and the standard deviation is 0.2 ounces.Test the complaint. ĐỀ 2
1. The amount of time devoted to studying statistics each week by students who
achieve a grade of A in one course is a normally distributed random variable with
a mean of 7.5 hours and a standard deviation of 2.1 hours.
a.What proportion of A students study for more than 10 hours per week?
b.What is the amount of time below which only 5% of all A students spend studying?
2. A survey of 400 statistics professors was undertaken. Each professor was
asked how much time was devoted to teaching graphical techniques.We believe
that the times are normally distributed with a standard deviation of 30
minutes.The average time of the survey is 120 minutes. Estimate the population mean with 95% confidence.
3. A medical statistician wants to estimate the average weight loss of people
who are on a new diet plan. In a preliminary study,he guesses that the standard
deviation of the population of n weight losses is about 10 pounds.How large a
sample should he take to estimate the mean weight loss to within 2 pounds.with 90%confidence?
4. The assembly line that produces an electronic component of a missile system
has historically resulted in a 2% defective rate.A random sample of 800
components is drawn.What is the probability that the defective rate is greater
than 4%? Suppose that in the random sample the defective rate is 4%. What does
that suggest about the defective rate on the assembly line?
5. A business student claims that.on average,an MBA student is required to
prepare more than five cases per week.To examine the claim,a statistics
professor asks a random sample of 10 MBA students to report the number of
cases they prepare weekly.The results are exhibited here: 2,7,4,8,9,5,11,3,7,4.Can
the professor conclude at the 5%significance level that the claim is true.
assuming that the number of cases is normally distributed with a standard deviation of 1.5?
6. A bottling company needs to produce bottles that will hold 12 ounces of liquid
for a local beer maker. Periodically,the company gets complaints that their
bottles are not holding 12 ounces of liquid. The bottling company randomly
samples 15 bottles and finds the average amount of liquid held by the 15 bottles
is 11.90 ounces and the standard deviation is 0.2 ounces. Test the complaint. ĐỀ 3
1.The marks on a statistics midterm test are normally distributed with a mean of
78 and a standard deviation of 6.
a.What proportion of the class has a midterm mark of less than 75?
b.What is the probability that a class of 50 has an average midterm mark that is less than 75?
2.A psychologist believes that 80%of male drivers when lost continue to drive
hoping to find the location they seek rather than ask directions.To examine this
belief, he took a random sample of 350 male drivers and asked each what they
did when lost. If the belief is true, determine the probability that less than 75% said they continue driving.
3.The label on 1-gallon cans of paint states that the amount of paint in the can is
sufÏcient to paint 400 square feet.However.this number is quite variable.In
fact,the amount of coverage is known to be approximately normally distributed
with a standard deviation of 25 square feet.
How large a sample should be taken to estimate the true mean coverage of ail l-
gallon cans to within 5 square feet with 95% confidence?
4.Most owners of digital cameras store their pictures on the camera. Some will
eventually download these to a computer or print them using their own printers
or a commercial printer. A film-processing company wanted to know how many
pictures were stored on computers. A random sample of 10 digital camera
owners produced the data given here: 25 6 22 26 31 18 13 20 14 2. Estimate with
95% confidence the mean number of pictures stored on digital cameras.
5.Spam email has become a serious and costly nuisance.An ofÏce manager
believes that the average amount of time spent by ofÏce workers reading and
deleting spam exceeds 25 minutes per day. To test this belief, he takes a random
sample of 18 workers and measures the amount of time each spends reading
and deleting spam.The results are listed here:35 48 29 44 17 21 32 28 34 23 139
11 30 42 37 43 48. If the population of times is normal with a standard deviation
of 12 minutes, can the manager inter at the 1% significance level that he is
correct? Compute the p- value of the test. ĐỀ 4
1.The number of pizzas consumed per month by university students is normally
distributed with a means of 10 and a standard deviation of 3
a.What proportion of students consume more than12 pizzas per month
b.What is the probability that in a random sample of 25 students more than 275 pizzas are consumed?
2.An accounting professor claims that no more than one-quarter of
undergraduate business students will major in accounting.What is the probability
that in a random sample of 1.200 undergraduate business students.336 or more will major in accounting?
3.A statistics professor wants to compare today's students with those 25 years
ago.All his current students' marks are stored on a computer so that he can
easily determine the population mean. However, the marks 25 years ago reside
only in his musty files. He does not want to retrieve all the marks and will be
satisfied with a 95% confidence interval estimate of the mean mark 25 years ago.
If he assumes that the population standard deviation is 12. How large a sample
should he take to estimate the mean to within 2 marks?
4.A parking control ofÏcer is conducting an analysis of the amount of time left on
parking meters.A quick survey of 15 cars that have just left their metered parking spaces produced the
following times (in minutes) 22 15 1 14 0 9 17 31 18 26 23 15 33 28 20. Estimate
with 95% confidence the mean amount of time left for all the city's meters.
5.A random sample of 12 second-year university students enrolled in a business
statistics course was drawn. At the course's completion,each student was asked
how many hours he or she spent doing homework in statistics.The data are listed
here:31 40 26 30 36 38 29 40 38 30 35 38. It is known that the population
standard deviation is 8.0.The instructor has recommended that students devote
3 hours per week for the duration of the 12-week semester, for a total of 36
hours.Test to determine whether there is evidence that the average student
spend less than the recommended amount of time.Compute the p-value of the test.