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21:11, 27/01/2026
Đề Giữa Kỳ và Cuối Kỳ XSTK CLC - Thầy Minh - Studocu ĐỀ GIỮA KỲ
1. Twenty-five weather stations measure rainfall at random locations in the state of
Hawaii. The population of rainfall is normally distributed. In 1995, these
twenty-five stations recorded an average rainfall of 12 inches with a standard
deviation of 1.2 inches. Construct a 95% confidence interval for the mean rainfall of this state in 1995.
2. To estimate the mean retail price of designer jeans, a buyer sampled 19 retailers
in New York City and recorded the selling price of the jeans.The following
statistics were reported: mean $51.75 and a standard deviation of S5.50. Which of
the following would represent a 99% confidence interval for the mean?
3. If we repeatedly draw samples of size 121 from the population of senior citizens,
90% of the values of sample means will be such that the population mean amount
of time senior citizens spend walking would be somewhere between 6.978 hours
and 9.022 hours per week, and 10% of the values of the sample mean will produce
intervals that would not include the population mean.
Determine the 99% confidence interval estimate of the population mean if the
sample size is changed to 225 .
4. The sample size needed to estimate a population mean to within 10 units was
found to be 68. If the population standard deviation was 50, then the confidence interval used was?
5. How large a sample of state employees should be taken if we want to estimate
with 95% confidence the mean salary to within $2,000? The population standard
deviation is assumed to be $10,500. 21:11, 27/01/2026
Đề Giữa Kỳ và Cuối Kỳ XSTK CLC - Thầy Minh - Studocu ĐỀ CUỐI KỲ 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. 21:11, 27/01/2026
Đề Giữa Kỳ và Cuối Kỳ XSTK CLC - Thầy Minh - Studocu 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. 21:11, 27/01/2026
Đề Giữa Kỳ và Cuối Kỳ XSTK CLC - Thầy Minh - Studocu 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
sufficient 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 office manager believes that
the average amount of time spent by office 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 i
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. 21:11, 27/01/2026
Đề Giữa Kỳ và Cuối Kỳ XSTK CLC - Thầy Minh - Studocu 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 officer 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. 21:11, 27/01/2026
Đề Giữa Kỳ và Cuối Kỳ XSTK CLC - Thầy Minh - Studocu