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22:13, 27/01/2026
Lí thuyết và bài tập ôn thi Final XSTK - Studocu TEST 1
a. (1 mark) Calculate the sample mean and standard deviation.
b. (1 mark) Contruct a 95 percent confidence interval for the population mean. Time: 60 minutes
c. (1 mark) Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pound
Question 1. (2 marks) In 2011, there were 1901 fatalities recorded on Britain’s roads, 60 of
? Use the 0.01 significance level.
which were for children (Department of Transport, 2012). Correspondingly, serious injuries
Question 5. (2 marks) Research in the gaming industry showed that 10 percent of all slo
totalled 23 122 of which 20 770 were for adults.
machines in the United States stop working each year. Short’s Game Arcade has 60 slo
a. (1 mark) What is the probability of a serious injury given the victim was a child?
machines and only 3 failed last year. Use the hypothesis-testing procedure at the 0.0
b. (1 mark) What is the probability that the victim was an adult given a fatality occurred?
significance level to test whether this data contradicts the research report. Question 2. (2 marks)
a. (1 mark) State the null and the alternative hypotheses.
The accounting department at Weston Materials Inc., a national manufacturer of unattached
b. (1 mark) What is the conclusion of the hypothesis testing?
garages, reports that it takes two construction workers a mean of 32 hours and a standard
deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.
a. (1 mark) What percent of the garages take between 29 hours and 34 hours to erect?
b. (1 mark) Of the garages, 5 percent take how many hours or more to erect? Question 3. (1 mark)
Using historical records, the personnel manager of a plant has determined the probability
distribution of X, the number of employees absent per day. It is X 0 1 2 3 4 5 6 7 P(X) 0,005 0,025 0,31 0,34 0,22 0,08 0,019 0,001
Calculate the mean and the standard deviation.
Question 4. (3 marks) Rutter Nursery Company packages its pine bark mulch in 50 pound
bags. From a long history, the production department reports that the distribution of the bag
weights follows the normal distribution and the standard deviation of this process is 3
pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags
and computes the mean weight of the sample. Below are the weights of 10 bags from today’s production.
45,6 47,7 47,6 46,3 46,2 47,4 49,2 55,8 47,5 48,5 22:13, 27/01/2026
Lí thuyết và bài tập ôn thi Final XSTK - Studocu TEST 2
Question 5. (2 marks) A survey of 750 university students found they were paying o Time: 60 minutes
average $108 per week in accommodation costs. Assume the population standard deviatio
Question 1. (2 marks) Data evidence shows that last year 25% of the stocks in a stock
for weekly accommodation costs is $22.
exchange performed well, 25% poorly, and the remaining 50% performed on average.
a. (1 mark) Construct a 90 per cent confidence interval estimate of the population mean.
Moreover, 40% of those that performed well were rated a “good buy” by a stock analyst, as
b. (1 mark) Construct a 95 per cent confidence interval estimate of the population mean.
were 20% of those that performed on average, and 10% of those that performed poorly.
a. (1 mark) What is the probability that a stock rated were rated a
Question 6. (2 marks) After many years of teaching, a statistics professor computed th “good buy"? 2
variance of the marks on her final exam and found it to be  = 250. She recently mad
b. (1 mark) What is the probability that a stock rated a “good buy" by the stock analyst will
changes to the way in which the final exam is marked and wondered whether this woul perform well this year?
result in a reduction in the variance. A random sample of this year’s final exam marks ar
Question 2. (2 marks) A recent report in USA Today indicated a typical family of four listed here.
spends $490 per month on food. Assume the distribution of food expenditures for a family 57 92 99 73 62 64 75 70 88 60
of four follows the normal distribution, with a mean of $490 and a standard deviation of $90.
a. (1 mark) Calculate the sample mean and variance.
a. (1 mark) What percent of the families spend more than $30 but less than $490 per month
b. (1 mark) Can the professor infer at the 10% significance level that the variance ha on food? decreased?
b. (1 mark) What percent of the families spend less than $430 per month on food?
Question 3. (1 mark) The following density function describes the random variable X.  x  x ; 0 5 25   f x  10 ; 5x 10  x    25  0 ; x 0 ;10 
Compute the probability that X is less than 7.
Question 4. (1 mark) A corporation is considering a new issue of convertible bonds.
Management believes that the offer terms will be found attractive by 20% of all its current
stockholders. Suppose that this belief is correct. A random sample of 130 current
stockholders is taken. What is the probability that the sample proportion is between 0.18 and 0.22? 22:13, 27/01/2026
Lí thuyết và bài tập ôn thi Final XSTK - Studocu TEST 3
Question 5. (1 mark) Fuel consumption tests are conducted for a particular model of car.
a 98 per cent confidence interval with a margin of error of 0.2 litres per 100km is desire Time: 60 minutes
how many cars should be used in the test? Assume that preliminary tests indicate th
Question 1. (2 marks) A union’s executive conducted a survey of its members to determine
standard deviation is 0.5 litres per 100km.
what the membership felt were the important issues to be resolved during upcoming
Question 6. (2 marks) Has the recent drop in airplane passengers resulted in better on-tim
negotiations with management. The results indicate that 74% of members felt that job
performance? Before the recent downturn one airline bragged that 92% of its flights were o
security was an important issue, whereas 65% identified pension benefits as an important
time. A random sample of 165 flights completed this year reveals that 153 were on tim
issue. Of those who felt that pension benefits were important, 60% also felt that job security
Can we conclude at the 5% significance level that the airline’s on-time performance ha
was an important issue. One member is selected at random. improved?
a. (1 mark) What is the probability that he or she felt that both job security and pension
a. (1 mark) State the null and the alternative hypotheses. benefits were important?
b. (1 mark) What is the conclusion of the hypothesis testing?
b. (1 mark) What is the probability that the member felt that at least one of these two issues was important?
Question 2. (2 marks) According to a Gallup poll 27% of American adults have confidence
in banks. Suppose that you interview 5 Americans adults at random.
a. (1 mark) What is the probability that 2 or fewer have confidence in banks?
b. (1 mark) What is the probability that no one had confidence in banks?
Question 3. (1 mark) A random variable has the following density function.  xx    f x  1 ;0 2  2   0  ; x 0; 2 
Calculate the mean and variance of the random variable.
Question 4. (2 marks) The weights of a random sample of cereal boxes that are supposed
to weigh 1 pound are listed here.
1,05 1,03 0,98 1,00 0,99 0,97 1,01 0,96
a. (1 mark) Calculate the sample mean and variance.
b. (1 mark) Assume the normality, estimate the variance of the entire population of cereal
box weights with 90% confidence. 22:13, 27/01/2026
Lí thuyết và bài tập ôn thi Final XSTK - Studocu TEST 4
Question 5. (2 marks) Consumption of alcoholic beverages by young women of drinkin
age is of concern in the UK and some other European countries. Annual consumption dat Time: 60 minutes
(in litres) are shown below for a sample of 20 European young women.
Question 1. (2 marks) In a large corporation, 80% of the employees are men and 20% are 266 82 199 174 97
women. The highest levels of education obtained by the employees are graduate training for 170 222 115 130 169
10% of the men, undergraduate training for 30% of the men, and high school training for 164 102 113 171 0
60% of the men. The highest levels of education obtained are also graduate training for 15%
of the women, undergraduate training for 40% of the women, and high school training for 93 0 93 110 130 45% of the women.
a. (1 mark) Calculate the sample mean and variance.
a. (1 mark) What is the probability that a randomly chosen employee will be a man with
a. (1 mark) Assuming normality, construct a 95% confidence interval for the mean annu only a high school education?
consumption of alcoholic beverages by young European women.
b. (1 mark) What is the probability that a randomly chosen employee who has graduate
Question 6. (2 marks) A random sample of 50 university admissions officers was aske training is a man?
about expectations in application interviews. Of these sample members, 28 agreed that th
Question 2. (2 marks) Andrew Whittaker, computer center manager, reports that his
interviewer usually expects the interviewee to have volunteer experience doing communit
computer system experienced three component failures during the past 100 days.
projects. Test that the population proportion is larger than one-half. Use  = 0.05.
a. (1 mark) What is the probability of no failures in a given day?
b. (1 mark) What is the probability of at least two failures in a 3-day period?
Question 3. (1 mark) Forest Green Brown, Inc., produces bags of cypress mulch. The
weight in pounds per bag varies, as indicated in the accompanying table. Weight 44 45 46 47 48 49 50 Proportion 0,04 0,13 0,21 0,29 0,2 0,1 0,03
The cost (in cents) of producing a bag of mulch is 75 + 2X, where X is the number of
pounds per bag. The revenue from selling the bag, regardless of weight, is $2.50. If profit is
defined as the difference between revenue and cost, find the mean and standard deviation of profit per bag.
Question 4. (1 mark) It is believed that first-year salaries for newly qualified accountants
follow a normal distribution with a standard deviation of $2,500. A random sample of 16
observations was taken. Find the probability that the sample standard deviation is more than $3,000. 22:13, 27/01/2026
Lí thuyết và bài tập ôn thi Final XSTK - Studocu TEST 5
c. (2 marks) Test that Internet executives have a mean stress level in the dangerous leve
according to Dr. Benner’s test? Use  = 0.05. Time: 60 minutes
Question 5. (1 mark) A random sample of 100 men contained 61 in favor of a sta
Question 1. (2 marks) Of 100 patients with a certain disease, 10 were chosen at random to
constitutional amendment to retard the rate of growth of property taxes. An independen
undergo a drug treatment that increases the cure rate from 50% for those not given the
random sample of 100 women contained 54 in favor of this amendment. A confidenc
treatment to 75% for those given the drug treatment.
interval extending from 0.04 to 0.10 was calculated for the difference between th
a. (1 mark) What is the probability that a randomly chosen patient both was cured and was
population proportions. Determine the confidence level of this interval. given the drug treatment?
b. (1 mark) What is the probability that a patient who was cured had been given the drug treatment?
Question 2. (2 marks) The amount of time devoted to studying statistics each week by
students who achieve a grade of A in the course is a normally distributed random variable
with a mean of 7.5 hours and a standard deviation of 2.1 hours.
a. (1 mark) What proportion of A students study for more than 10 hours per week?
b. (1 mark) What is the amount of time below which only 5% of all A students spend studying?
Question 3. (1 mark) We are given the following probability distribution. X 0 1 2 3 P(x) 0,4 0,3 0,2 0,1
Suppose that Y = 3X + 2. What is the probability distribution of Y ?
Question 4. (4 marks) Dr. Susan Benner is an industrial psychologist. She is currently
studying stress among executives of Internet companies. She has developed a questionnaire
that she believes measures stress. A score above 80 indicates stress at a dangerous level. A
random sample of 15 executives revealed the following stress level scores.
94, 78, 83, 90, 78, 99, 97, 90, 93, 100, 75, 84
a. (1 mark) Calculate the sample mean and variance.
b. (1 mark) Assume normality, construct a 98 percent confidence level for the population mean. 22:13, 27/01/2026
Lí thuyết và bài tập ôn thi Final XSTK - Studocu