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Questions and Answers of
Business Statistics
If five dice are rolled, how many different outcomes are there?
Three bands and two comics are performing for a student talent show. How many different programs (in terms of order) can be arranged? How many if the comics must perform between bands?
A lottery game called Quinto is played by choosing five numbers each, from 0 through 9. How many numbers are possible? Although repeats are allowed, how many numbers are possible if repeats are not
How many different ways can a visiting nurse visit 9 patients if she wants to visit them all in one day?
Seven elementary students are selected to give a 3-minute presentation on what they did during summer vacation. How many different ways can the speakers be arranged?
List all the permutations of the letters in the word MATH.
How many 5-digit zip codes are possible if digits can be repeated? If there cannot be repetitions?
Two bags contain marbles. Bag 1 contains 1 black marble and 9 white marbles. Bag 2 contains 1 black marble and x white marbles. If you choose a bag at random, then choose a marble at random, the
In a child’s board game of the tortoise and the hare, the hare moves by roll of a standard die and the tortoise by a six-sided die with the numbers 1, 1, 1, 2, 2, and 3. Roll each die once. What is
Given a sample space with events A and B such that P(A) = 0.342, P(B) = 0.279, and P(A or B) = 0.601. Are A and B mutually exclusive? Are A and B independent? Find P(A|B), P(not B), and P(A and B).
Let A and B be two mutually exclusive events. Are A and B independent events? Explain your answer.
In a large vase, there are 8 roses, 5 daisies, 12 lilies, and 9 orchids. If 4 flowers are selected at random, and not replaced, find the probability that at least 1 of the flowers is a rose. Would
Twelve percent of people in Western countries consider themselves lucky. If 3 people are selected at random, what is the probability that at least one will consider himself lucky?
As of June 2015, 81.4% of patients were waiting on a kidney, 11.7% were waiting on a liver, and 3.1% were waiting on a heart. Choose 6 patients on the transplant waiting list at random in 2015. Find
A die is rolled twice. Find the probability of getting at least one 6.
If 3 digits are selected at random with replacement, find the probability of getting at least one odd number. Would you consider this event likely or unlikely? Why?
A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least 1 person’s infection will not improve.
Video games are rated according to the content. The average age of a gamer is 35 years old. In 2015, 15.5% of the video games were rated Mature. Choose 5 purchased games at random. Find the
In recent years it was thought that approximately 1 in 110 children exhibited some form of autism. The most recent CDC study concluded that the proportion may be as high as 1 in 88. If indeed these
If 5 cards are drawn at random from a deck of 52 cards and are not replaced, find the probability of getting at least one diamond.
According to FlightStats report released April 2013, the Salt Lake City airport led major U.S. airports in on-time arrivals with an 85.5% on-time rate. Choose 5 arrivals at random and find the
According to the Statistical Abstract of the United States, 70.3% of females ages 20 to 24 have never been married. Choose 5 young women in this age category at random. Find the probability thata.
In a department store there are 120 customers, 90 of whom will buy at least 1 item. If 5 customers are selected at random, one by one, find the probability that all will buy at least 1 item.
It has been said that the probability of being struck by lightning is about 1 in 750,000, but under what circumstances? Below are listed the numbers of deaths from lightning since 1996.Choose one
In a pizza restaurant, 95% of the customers order pizza. If 65% of the customers order pizza and a salad, find the probability that a customer who orders pizza will also order a salad.
Below is given the summary from the 112th Congress of Senators whose terms end in 2013, 2015, or 2017.Choose one of these Senators at random and finda. P(Democrat and term expires in 2015)b.
At a large university, the probability that a student takes calculus and is on the dean’s list is 0.042. The probability that a student is on the dean’s list is 0.21. Find the probability that
At the Avonlea Country Club, 73% of the members play bridge and swim, and 82% play bridge. If a member is selected at random, find the probability that the member swims, given that the member plays
Twenty-five percent of all deaths (all ages) are caused by diseases of the heart. Ischemic heart disease accounts for 16.4% of all deaths and heart failure for 2.3%. Choose one death at random. What
Roll two standard dice and add the numbers. What is the probability of getting a number larger than 9 for the first time on the third roll?
For a recent year, 0.99 of the incarcerated population is adults and 0.07 of the incarcerated are female. If an incarcerated person is selected at random, find the probability that the person is a
Urn 1 contains 5 red balls and 3 black balls. Urn 2 contains 3 red balls and 1 black ball. Urn 3 contains 4 red balls and 2 black balls. If an urn is selected at random and a ball is drawn, find the
In a box of 12 batteries, 2 are dead. If 2 batteries are selected at random for a flashlight, find the probability that both are dead. Would you consider this event likely or unlikely?
At a gathering consisting of 10 men and 20 women, two door prizes are awarded. Find the probability that both prizes are won by men. The winning ticket is not replaced. Would you consider this event
In a scientific study there are 8 guinea pigs, 5 of which are pregnant. If 3 are selected at random without replacement, find the probability that all are pregnant.
Four cards are drawn from a desk without replacement. Find these probabilities.a. All cards are jacks.b. All cards are black cards.c. All cards are hearts.
A flashlight has 6 batteries, 2 of which are defective. If 2 are selected at random without replacement, find the probability that both are defective.
Smart TVs have seen success in the United States market. During the 2nd quarter of 2015 45% of TVs sold in the United States were Smart TVs. That’s an increase of 11% from 2014. Choose three
A bag contains 9 red marbles, 8 white marbles, and 6 blue marbles. Randomly choose two marbles, one at a time, and without replacement. Find the following.a. The probability that the first marble is
Seventy-five percent of female prison inmates are mothers. If 3 female prison inmates are selected at random, what is the probability that none are mothers?
In 2013 about 66% of full-time law enforcement workers were sworn officers, and of those, 88.4% were male. Females however make up 60.7% of civilian employees. Choose one law enforcement worker at
If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that 2 randomly selected federal prison inmates will not be U.S. citizens.
The Gallup Poll reported that 52% of Americans used a seat belt the last time they got into a car. If 4 people are selected at random, find the probability that they all used a seat belt the last
Events A and B are mutually exclusive with P(A) equal to 0.392 and P(A or B) equal to 0.653. Finda. P(B)b. P(not A)c. P(A and B)
The probability of event A occurring is m/(2m + n), and the probability of event B occurring is n/(2m + n). Find the probability of A or B occurring if the events are mutually exclusive.
For a recent year, about 11 billion pounds of apples were harvested. About 4.4 billion pounds of apples were made into apple juice, about 1 billion pounds of apples were made into apple sauce, and 1
Suppose that P(A) = 0.42, P(B) = 0.38, and P(A or B) = 0.70. Are A and B mutually exclusive? Explain.
In Exercise 28, find the probability that the buyer will not want a two-car garage.In exerciseIn building new homes, a contractor finds that the probability of a home buyer selecting a two-car garage
The probability that a customer selects a pizza with mushrooms or pepperoni is 0.55, and the probability that the customer selects only mushrooms is 0.32. If the probability that he or she selects
If one card is drawn from an ordinary deck of cards, find the probability of getting each event:a. A 7 or an 8 or a 9b. A spade or a queen or a kingc. A club or a face cardd. An ace or a diamond or a
The data show the U.S. population by age.Under 20 years...............27.0%20 years and over..............73.065 years and over..............13.1Choose one person from the United States at random.
The following doctors were observed on staff at a local hospital.Choose one doctor at random; what is the probability thata. She is a pathologist?b. He is an orthopedist or an MD? Doctor of
The probability that John will drive to school is 0.37, the probability that he will ride with friends is 0.23, and the probability that his parents will take him is 0.4. He is not allowed to have
Determine whether these events are mutually exclusive.a. Roll two dice: Get a sum of 7 or get doubles.b. Select a student in your college: The student is a sophomore and the student is a business
During a recent year, there were 13.5 million automobile accidents, 5.2 million truck accidents, and 178,000 motorcycle accidents. If one accident is selected at random, find the probability that it
Here are the living arrangements of children under 18 years old living in the United States in a recent year. Numbers are in thousands.Both parents..........................51,823Mother
The numbers show the number of crimes committed in a large city. If a crime is selected at random, find the probability that it is a motor vehicle theft. What is the probability that it is not an
The population of Hawaii is 22.7% white, 1.5% African-American, 37.7% Asian, 0.2% Native American/Alaskan, 9.46% Native Hawaiian/Pacific Islander, 8.9% Hispanic, 19.4% two or more races, and 0.14%
In a game of craps, a player wins on the first roll if the player rolls a sum of 7 or 11, and the player loses if the player rolls a 2, 3, or 12. Find the probability that the game will last only one
A couple has 4 children. Find each probability.a. All girlsb. Exactly two girls and two boysc. At least one child who is a girld. At least one child of each gender
Of all of the U.S. album sales 1989 (Taylor Swift) accounted for 25% of sales, Frozen (Various Artists) accounted for 24.1% of sales, In the Lonely Hour (Sam Smith) accounted for 8.2% of sales. What
If one card is drawn from a deck, find the probability of getting these results:a. An aceb. A heartc. A 6 of spadesd. A 10 or a jacke. A card whose face values less than 7 (Count aces as 1.)
If two dice are rolled one time, find the probability of getting these results:a. A sum less than 9b. A sum greater than or equal to 10c. A 3 on one die or on both dice.
If two dice are rolled one time, find the probability of getting these results:a. A sum of 5b. A sum of 9 or 10c. Doubles
If a die is rolled one time, find these probabilities:a. Getting a number less than 7.b. Getting a number greater than or equal to 3c. Getting a number greater than 2 and an even numberd. Getting a
If a die is rolled one time, find these probabilities:a. Getting a 7b. Getting an odd numberc. Getting a number less than 7d. Getting a prime number (2, 3, or 5)
Classify each statement as an example of classical probability, empirical probability, or subjective probability.a. The probability that a student will get a C or better in a statistics course is
A probability experiment is conducted. Which of these cannot be considered a probability outcome?a. 2/3b. 0.63c. − 3/5d. 1.65e. − 0.44f. 0g. 1h. 125%i. 24%
If the probability that it will rain tomorrow is 0.20, what is the probability that it won’t rain tomorrow? Would you recommend taking an umbrella?
What is the sum of the probabilities of all the outcomes in a sample space?
If an event cannot happen, what value is assigned to its probability?
When an event is certain to occur, what is its probability?
What is the range of the values of the probability of an event?
What are equally likely events?
What is the difference between an outcome and an event?
Define sample space.
What is a probability experiment?
The data show the number of named storms for the years 18511860 and 1941 and 1950. Construct a boxplot for each data set and compare the distributions. 1851–1860 1941–1950 6 5 8 5 5 6
The frequency distribution shows the number of days it took to fix each of 80 computer’s printers.Class limits Frequency1–3
The number of police calls a small police department received each month is shown in the frequency distribution.Class limits
The data show the number of specific recorded cases of meningitis for 14 specific states.Find the z values for eacha. 10b. 28c. 41 10 1 1 28 15 41 4 4 8 2 3 53 34 1
The mean time it takes a group of students to complete a statistics final exam is 44 minutes, and the standard deviation is 9 minutes. Within what limits would you expect approximately 95% of the
The average cost of a man’s haircut is $21. The standard deviation is $4. If the variable is approximately bell-shaped, within what limits would 68% of the haircut cost?
If the range of a data set is 56, find the approximate value of the standard deviation, using the range rule of thumb.
If the range of a data set is 24, find the approximate value of the standard deviation, using the range rule of thumb.
The data show a sample of the number of confirmed measles cases over a recent 12-year period. Find the range, variance, and standard deviation for the data. 212 44 43 55 63 71 66 37 140 56 86 116
The data show the systolic blood pressure of 30 college students. Find the mean and modal class.Class
The data show the number of bank failures over a 15-year period. Find the mean, median, midrange, and mode for the data. 14 24 51 92 157 148 30 3 0 0 4 3 11 4 7
A four-month record for the number of tornadoes in 20132015 is given here.a. Which month had the highest mean number of tornadoes for this 3-year period? May:b. Which year has the highest
The data show the heights (in feet) of the 10 largest dams in the United States. Identify the five-number summary and the interquartile range, and draw a boxplot. 770 730 717 710 645 606 602 585 578
The data show the sizes in square miles of notable islands in the Baltic Sea and the Aleutian Islands. Construct a boxplot for each data set and compare the distributions.Baltic Sea
The data show the population (in thousands) of the U.S. Colonies in 1700 (Vermont was not a colony until 1791). Construct a boxplot and decide if the distribution is symmetric. 26.0 2.5 29.6 55.9 5.0
Construct a boxplot for the following data which represent the number of innings pitched by the ERA leaders for the past few years. Comment on the shape of the distribution. 239 249 266 251 245 238
The data show a sample of states percentage of public high school graduation rates for a recent year. Construct a boxplot for the data, and comment on the shape of the distribution. 79 82
Identify the five-number summary and find the interquartile range.9.7, 4.6, 2.2, 3.7, 6.2, 9.4, 3.8
Identify the five-number summary and find the interquartile range.14.6, 19.8, 16.3, 15.5, 18.2
A particular standardized test has scores that have a mound-shaped distribution with mean equal to 125 and standard deviation equal to 18. Tom had a raw score of 158, Dick scored at the 98th
An employment evaluation exam has a variance of 250. Two particular exams with raw scores of 142 and 165 have z scores of −0.5 and 0.955, respectively. Find the mean of the distribution.
Check each data set for outliers.a. 46, 28, 32, 21, 25, 29, 34, 19b. 82, 100, 97, 93, 89, 90, 65, 94, 101c. 527, 1007, 489, 371, 175
The data show the gold reserves for a recent year for 11 world countries. Find the first and third quartiles and the IQR. The data are in millions of troy ounces. 33.9 78.3 108.9 17.9 78.8 24.6 19.7
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