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mathematics
statistics

Questions and Answers of Statistics

If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that(a) The dictionary is selected?(b) 2 novels and 1 book of poems are
In a poker hand consisting of 5 cards, find the probability of holding(a) 3 aces;(b) 4 hearts and 1 club.
In a game of Yahtzee, where 5 dice are tossed simultaneously, find the probability of getting 4 of a kind.
In a high school graduating class of 100 students, 54 studied mathematics, 69 studied history, and 35 studied both mathematics and history. If one of these students is selected at random, find the
Dom's Pizza Company uses taste testing and statistical analysis of the data prior to marketing any new product. Consider a study involving three types of crusts (thin, thin with garlic and oregano,
According to Consumer Digest (July/August 1996), the probable location of personal computers (PC) in the home is as follows:Adult bedroom: 0.03Child bedroom: 0.15Other bedroom: 0.14Office or den:
Interest centers around the life of an electronic component. Suppose it is known that the probability that the component survives for more than 6000 hours is 0.42. Suppose also that the probability
Consider the situation of Exercise 2.68. Let A be the event that the component fails a particular test and B be the event that the component displays strain but does not actually fail. Event A occurs
Factory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur because the working environment or conditions themselves are unsafe.
Consider the situation of Example 2.31. (a) What is the probability that no more than 4 cars will be serviced by the mechanic?(b) What is the probability that he will service fewer than 8 cars?(c)
Interest centers around the nature of an oven purchased at a particular department store. It can be either a gas or electric oven. Consider the decision made by six distinct customers.(a) Suppose
It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for
Consider the situation of Exercise 2.73. Suppose 50,000 boxes of detergent are produced per week and suppose also that those under filled are "sent back" with customers requesting reimbursement of
As the situation of Exercise 2.73 might suggest, statistical procedures are often used for control of quality (i.e., industrial quality control). At times, the weight of a product is an important
Prove that P(A' n B') = 1 + P{A ∩ B) – P(A) – P{B}.
If R is the event that a convict committed armed robbery and D is the event that the convict pushed dope, state in words what probabilities are expressed by(a) P (R\D);(b) P (D'\R);(c) P (R'\D').
A class in advanced physics is comprised of 10 juniors, 30 seniors, and 10 graduate students. The final grades show that 3 of the juniors, 10 of the seniors, and 5 of the graduate students received
A random sample of 200 adults is classified below by sex and their level of education attained.If a person is picked at random from this group, find the probability that(a) The person is a male,
In an experiment to study the relationship of hypertension and smoking habits, the following data are collected for 180 individuals: where H and NH in the table stand for Hypertension and
In the senior year of a high school graduating class of 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both
A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.10, 0.08, and 0.12,
In USA Today (Sept. 5, 1996) the results of a survey involving the use of sleepwear while traveling were listed as follows:(a) What is the probability that a traveler is a female who sleeps in the
The probability that an automobile being filled with gasoline will also need an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and
The probability that a married man watches a certain television show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that
For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that his wife will vote in the referendum is 0.28, and the
The probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.12; the probability that it is a camper is 0.28; and the probability that it is a camper with Canadian
The probability that the head of a household is home when a telemarketing representative calls is 0.4. Given that the head of the house is home, the probability that goods will be bought from the
The probability that a doctor correctly diagnoses a particular illness is 0.7. Given that the doctor makes an incorrect diagnosis, the probability that the patient enters a law suit is 0.9. What is
In 1970, 11% of Americans completed four years of college; 43% of them were woman. In 1990, 22% of Americans completed four years of college; 53% of them were women (Time, Jan. 19, 1996).(a) Given
A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 40% of these homes are usually left unlocked, what is the probability that the real
Before the distribution of certain statistical software every fourth compact disk (CD) is tested for accuracy. The testing process consists of running four independent programs and checking the
A town has 2 fire engines operating independently. The probability that a specific engine is available when needed is 0.96.(a) What is the probability that neither is available when needed?(b) What
The probability that Tom will be alive in 20 years is 0.7, and the probability that Nancy will be alive in 20 years is 0.9. If we assume independence for both, what is the probability that neither
One overnight case contains 2 bottles of aspirin and 3 bottles of thyroid tablets. A second tote bag contains 3 bottles of aspirin, 2 bottles of thyroid tablets, and I bottle of laxative tablets. If
The probability that a person visiting his dentist will have an X-ray is 0.6; the probability that a person who has an X-ray will also have a cavity filled is 0.3; and the probability that a person
Find the probability of randomly selecting 4 good quarts of milk in succession from a cooler containing 20 quarts of which 5 have spoiled, by using(a) The first formula of Theorem 2.15 on page 64;(b)
Suppose the diagram of an electrical system is given in Figure. What is the probability that the system works? Assume the components fail independently.
A circuit system is given in Figure. Assume the components fail independently.(a) What is the probability that the entire system works?(b) Given that the system works, what is the probability that
In the situation of Exercise 2.99, it is known that the system does not work. What is the probability that the component A also floes not work?
In a certain region of the country it is known from (last, experience that the: probability of selecting an adult over 40 years of age: with cancer is 0.05, If the probability of a doctor correctly
Police plan to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each of the locations L\, L2, L3, and L4 are operated 40%, 30%, 20%, and
Referring to Exercise 2.101, what, is the probability that a person diagnosed as having cancer actually has the disease?
If in Exercise 2.102 the person received a speeding ticket on his way to work, what is the probability that he passed through the radar trap located at L2?
Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to
A regional telephone company operates three identical relay stations at different locations. During a one year period, the number of malfunctions reported by each station and the causes are shown
Pollution of the rivers in the United States has been a problem for many years. Consider the following events:A = (The river is polluted.}B = {A sample of water tested detects pollution.}C = {Fishing
A paint-store chain produces and sells latex and semi gloss paint. Based on long-range sales, the probability that a customer will purchase latex paint is 0.75. Of those that purchase latex paint,
A truth serum has the property that 90% of the guilty suspects are properly judged while, of course, 10% of guilty suspects are improperly found innocent. On the other hand, innocent suspects are
An allergist claims that 50% of the patients she tests are allergic to some type of weed. What is the probability that (a) Exactly 3 of her next 4 patients are allergic to weeds?(b) None of her next
The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively, find the
How many bridge hands are possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts?
If the probability is 0.1 that a person will make a mistake on his or her state income tax return, find the probability that(a) Four totally unrelated persons each make a mistake;(b) Mr. Jones and
A large industrial firm uses 3 local motels to provide overnight accommodations for its clients. From past experience it is known that 20%: of the clients are assigned rooms at the Ramada Inn, 50% at
From a group of 4 men and 5 women, how many committees of size 3 are possible(a) With no restrictions?(b) With 1 man and 2 women?(c) With 2 men and 1 woman if a certain man must be on the committee?
The probability that a patient recovers from a delicate heart operation is 0.8. What is the probability that(a) Exactly 2 of the next 3 patients who have this operation survive?(b) All of the next 3
In a certain federal prison it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age
From 4 red, 5 green, and 6 yellow apples, how many selections of 9 apples are possible if 3 of each color are to be selected?
From a box containing 6 black balls and 4 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made. What is the probability that(a) All 3 are the
A shipment of 12 television sets contains 3 defective sets. In how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets? Discuss.
Electrical, chemical, industrial, and mechanical engineering curricula were studied. It was found that some students took no statistics, some took one semester, and others took two semesters.
A certain federal agency employs three consulting firms (A, B, and C) with probabilities 0.40, 0.35, and 0.25, respectively. From past experience it is known that the probability of cost overruns for
A manufacturer is studying the effects of cooking temperature, cooking time, and type of cooking oil for making potato chips. Three different temperatures, 4 different cooking times, and 3 different
Consider the situation in Exercise 2.124, and suppose that the manufacturer can try only two combinations in a day.(a) What is the probability that any given set of 2 runs is chosen?(b) What is the
A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease but the test is not infallible. In fact, it is known that
A producer of a certain type of electronic component ships to suppliers in lots of twenty. Suppose that 60% of all such lots contain no defective components, 30% contain one defective component, and
A rare disease exists in which only 1 in 500 are affected. A test for the disease exists but of course it is not infallible. A correct positive result (patient actually has the disease) occurs 95% of
A construction company employs 2 sales engineers. Engineer 1 does the work in estimating cost for 70% of jobs bid by the company. Engineer 2 does the work for 30% of jobs bid by the company. It is
In the field of quality control the science of statistics is often used to determine if a process is "out of control." Suppose the process is, indeed, out of control and 20% of items produced are
An industrial plant is conducting a study to determine how quickly injured workers are back on the job following injury. Records show that 10% of all injured workers are admitted to the hospital for
A firm is accustomed to training operators who do certain tasks on a production line. Those operators who attend the training course are known to be able to meet their production quotas 90% of the
A survey of those using a particular statistical software system indicated that 10% were dissatisfied. Half of those dissatisfied purchased the system from vender A. It is also known that 20%> of
During bad economic times, industrial workers are dismissed and are often replaced by machines. The history of 100 workers whose loss of employment is attributable to technological advances is
There is a 50-50 chance that the queen carries the gene of hemophilia. If she is a carrier, then each prince has a 50-50 chance of having hemophilia independently. If the queen is not a carrier, the
What is the probability that no two students will have the same birth date in a size of 60 classes?
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.3.4 2.5 4.8 2.9 3.62.8 3.3 5.6 3.7 2.84.4 4.0 5.2 3.0 4.8Assume that the measurements are a
According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 pieces of cotton fiber is taken and the absorbency on each piece was
A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be resistant to the aging process. Twenty specimens of the polymer were used in an experiment. Ten were
In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods
Twenty adult males between the ages of 30 and 40 were involved in a study to evaluate the effect of a specific health regimen involving diet and exercise on the blood cholesterol. Ten were randomly
The tensile strength of silicone rubber is thought to be a function of curing temperature. A study was carried out in which samples of 12 specimens of the rubber were prepared using curing
Consider the drying time data for Exercise 1.1, compute the sample-variance and sample standard deviation.
Compute the sample variance: and standard deviation for the water absorbency data of Exercise 1.2.
Exercise 1.3 showed samples of tensile strength data, one for specimens that were exposed to an aging process and one in which there was no aging of the specimens. Calculate the sample variance as
For the data of Exercise 1.4 compute both the mean and variance in flexibility for berth company A and company B.
Consider the data in Exercise 1.5. Compute the sample variance and the sample standard deviation for both the control and treatment groups.
For Exercise 1.6, compute the sample standard deviation in tensile strength for the samples separately for the two temperatures. Does it, appear as in an increase in temperatures influences the
A manufacturer of electronic components is interested in determining the lifetime of a certain type of battery. A sample, in hours of life, is as follows: 123, 116, 122, 110, 175, 120, 125, 111, 118,
A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter would be 570 mm. The data are as follows: 572, 572, 573, 568, 569, 575, 565, 570?(a) Find
Five independent coin tosses result in HIIHHII. It turns out that if the coin is fair the probability of this outcome is (l/2)5 = 0.03125. Does this produce strong evidence that the coin is not fair?
A study of the effects of smoking on sleep patterns is conducted. The measure observed is the time in minutes that it takes to fall asleep. These data are obtained:(a) Find the sample mean for each
The following scores represent the final examination grade for an elementary statistics course:(a) Construct a stem-and-leaf plot for the examination grades in which the stems are 1, 2, 3,. . . 9.(b)
The following data represent the length of life in years, measured to the nearest tenth, of 39 similar fuel pumps:(a) Construct a stem-and-leaf plot for the life in years of the fuel pump using the
The following data represent the length of life, in seconds, of 50 fruit flies subject to a new spray in a controlled laboratory experiment:(a) Construct a double-stem-and-leaf plot for the life span
The nicotine contents, in milligrams, for 40 cigarettes of a certain brand were recorded as follows:(a) Find the sample mean and sample median.(b) Find the sample standarddeviation.
The following data are the measures of the diameters of 36 rivet heads in 1/100 of an inch.(a) Compute the sample mean and sample standard deviation.(b) Construct a relative frequency histogram of
The hydrocarbon emissions at idling speed in parts per million (ppm) for automobiles of 1980 and 1990 are given for 20 randomly selected cars.(a) Construct a dot plot as in Figure 1.1.(b) Compute the
The following are historical data on staff salaries (dollars per pupil on 30 schools sampled in the eastern part of the United States in the early 1970s).(a) Compute the sample mean and sample
The following data set is related to that in Exercise 1.24. It gives the percent of the families that are in the upper income level at the same individual schools in the same order as in Exercise
Suppose it is of interest to use the data sets in Exercises 1.24 and 1.25 to derive a model that would predict staff salaries as a function of percent of families in a high income level for current
A study is done to determine the influence of the wear, y, of a bearing as a function of the load, a;, on the bearing. A designed experiment is used for this study. Three levels of load were used,

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