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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

Are events A and B disjoint?Use the information that, for events A and B, we have P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.1.
Are events A and B independent?Use the information that, for events A and B, we have P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.1.
Find P(not A).Use the information that, for events A and B, we have P(A) = 0.8, P(B) = 0.4, and P(A and B) = 0.25.
We wish to find a model to predict levels of beta-carotene in the blood, which is the variable BetaPlasma in the dataset NutritionStudy, using the following variables as potential predictors: Age,
The commute is about 27 miles round trip, but actual biking distances, Distance, ranged from 25.86 to 27.52 miles. Output regressing Distance on BikeSteel is given below. Is the predicted distance
Use the information that, for events A and B, we have P(A) = 0.8, P(B) = 0.4, and P(A and B) = 0.25.Find P(A or B).
Use the information that, for events A and B, we have P(A) = 0.8, P(B) = 0.4, and P(A and B) = 0.25.Find P(A if B).
Use the information that, for events A and B, we have P(A) = 0.8, P(B) = 0.4, and P(A and B) = 0.25.Find P(B if A).
Use the information that, for events A and B, we have P(A) = 0.8, P(B) = 0.4, and P(A and B) = 0.25.Are events A and B disjoint?
Use the information that, for events A and B, we have P(A) = 0.8, P(B) = 0.4, and P(A and B) = 0.25.Are events A and B independent?
Use the fact that we have independent events A and B with P(A) = 0.7 and P(B) = 0.6.Find P(A if B).
Use the fact that we have independent events A and B with P(A) = 0.7 and P(B) = 0.6.Find P(B if A).
Use the fact that we have independent events A and B with P(A) = 0.7 and P(B) = 0.6.Find P(A and B).
Use the fact that we have independent events A and B with P(A) = 0.7 and P(B) = 0.6.Find P(A or B).
Table 11.3 gives probabilities for various combinations of events A, B, and their complements.Table 11.3Find P(A). not A 0.4 B 0.2 not B 0.1 0.3
Table 11.3 gives probabilities for various combinations of events A, B, and their complements.Table 11.3Find P(A and B). not A 0.4 B 0.2 not B 0.1 0.3
The US Social Security Administration collects information on the life expectancy and death rates of the population. Table 11.6 gives the number of US men out of 100,000 born alive who will survive
Table 11.3 gives probabilities for various combinations of events A, B, and their complements.Table 11.3Are events A and B independent? not A 0.4 B 0.2 not B 0.1 0.3
Table 11.3 gives probabilities for various combinations of events A, B, and their complements.Table 11.3Find P(B if A). not A 0.4 B 0.2 not B 0.1 0.3
Table 11.3 gives probabilities for various combinations of events A, B, and their complements.Table 11.3Find P(A if B). not A 0.4 B 0.2 not B 0.1 0.3
Table 11.3 gives probabilities for various combinations of events A, B, and their complements.Table 11.3Find P(A or B). not A 0.4 B 0.2 not B 0.1 0.3
Table 11.3 gives probabilities for various combinations of events A, B, and their complements.Table 11.3Find P(not B). not A 0.4 B 0.2 not B 0.1 0.3
Draw three skittles (possible colors: yellow, green, red, purple, and orange) from a bag. Let A be the event that all three skittles are green and B be the event that at least one skittle is
South Africa plays Australia for the championship in the Rugby World Cup. Let A be the event that Australia wins and B be the event that South Africa wins. (The game cannot end in a tie.)State
South Africa plays Australia for the championship in the Rugby World Cup. At the same time, Poland plays Russia for the World Team Chess Championship. Let A be the event that Australia wins their
Suppose that the probability function in Table 11.13 reflects the possible lifetimes (in months after emergence) for fruit flies.Table 11.13(a) What proportion of fruit flies die in their second
Roll two (six-sided) dice. Let A be the event that the first die is a 3 and B be the event that the sum of the two dice is 8.State whether the two events (A and B) described are disjoint,
Each of the following statements demonstrate a common misuse of probability. Explain what is wrong with each statement:(a) Approximately 10% of adults are left-handed. So, if we take a simple random
About 20% of movies coming out of Hollywood are comedies, Warner Bros has been the lead studio for about 9% of recent movies, and about 2% of recent movies are comedies from Warner Bros. Let C denote
Of the 213 countries or independent economies in the world recognized by the World Bank, 19% are classified by the World Bank as being developed. Are countries with a large land area more likely to
From its founding through 2012, the Rock and Roll Hall of Fame has inducted 273 groups or individuals. Table 11.4 shows how many of the inductees have been female or have included female members and
From its founding through 2012, the Hockey Hall of Fame has inducted 251 players. Table 11.5 shows number of players by place of birth and by position played. If a player is chosen at random from all
In a bag of peanut M & M’s, there are 80 M & Ms, with 11 red ones, 12 orange ones, 20 blue ones, 11 green ones, 18 yellow ones, and 8 brown ones. They are mixed up so that each candy piece
As in Exercise 11.36, we have a bag of peanut M & M’s with 80 M & Ms in it, and there are 11 red ones, 12 orange ones, 20 blue ones, 11 green ones, 18 yellow ones, and 8 brown ones. They
During the 2010-11 NBA season, Ray Allen of the Boston Celtics had a free throw shooting percentage of 0.881. Assume that the probability Ray Allen makes any given free throw is fixed at 0.881, and
The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the
Approximately 7% of men and 0.4% of women are red-green color-blind (as in Exercise 11.39). Assume that a statistics class has 15 men and 25 women.(a) What is the probability that nobody in the class
The Standard and Poor 500 (S&P 500) is a weighted average of the stocks for 500 large companies in the United States. It is commonly used as a measure of the overall performance of the US stock
A friend makes three pancakes for breakfast. One of the pancakes is burned on both sides, one is burned on only one side, and the other is not burned on either side. You are served one of the
Complete each tree diagram by filling in the missing entries (marked with a €˜€˜?€). 0.0598 Case A 0.23 Case B 0.77 0.2002 Case I 0.3268 Case A Case II Case B 0.43 0.24
Complete each tree diagram by filling in the missing entries (marked with a €˜€˜?€). 0.09 Case A Case B Case 0.18 Case A Case II Case B 0.45 Case III 0.268 Case A 0.67
Complete each tree diagram by filling in the missing entries (marked with a €˜€˜?€). Case A Case B 0.225 Case C Case I 0.16 · 0.45 Case II Case A Case B 0.025 Case C
Find the requested probabilities using the tree diagram inFigure 11.4.P(S) 0.9 A 0.1 0.6 0.4 0.2 0.8
P(A if S)Find the requested probabilities using the tree diagram in Figure 11.4. 0.9 A 0.1 0.6 0.4 0.2 0.8
P(B if R)Find the requested probabilities using the tree diagram in Figure 11.4. 0.9 A 0.1 0.6 0.4 0.2 0.8
According to the 2010 US Census, 65% of housing units in the US are owner-occupied while the other 35% are renteroccupied. Table 11.7 shows the probabilities of the number of occupants in a housing
People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent
The mammogram is helpful for detecting breast cancer in its early stages. However, it is an imperfect diagnostic tool. According to one study, 86.6 of every 1000 women between the ages of 50 and 59
Use the probability function given in the table to calculate:(a) The mean of the random variable(b) The standard deviation of the random variable 10 20 30 p(x) 0.7 0.2 0.1
Table 11.11 in Exercise 11.83 gives the probability function for the random variable giving the household size for an owner-occupied housing unit in the US.Table 11.11(a) Find the mean household
To find the proportion of times something occurs, we divide the count (often a binomial random variable) by the number of trials n. Using the formula for the mean and standard deviation of a binomial
Suppose that past experience shows that about 10% of passengers who are scheduled to take a particular flight fail to show up. For this reason, airlines sometimes overbook flights, selling more
As we see in Exercise 11.38 on page 653, during the 2010-11NBA season, Ray Allen of the Boston Celtics had a free throw shooting percentage of 0.881. Assume that the probability Ray Allen makes any
Exercise 11.121 describes a random variable that counts the number of owneroccupied units in a sample of housing units. Use the information in that exercise to find the mean and standard deviation of
Exercise 11.120 describes a random variable that counts the number of senior citizens in a sample. Use the information in that exercise to find the mean and standard deviation of this random
Exercise 11.119 describes a random variable that counts the number of college graduates in a sample. Use the information in that exercise to find the mean and standard deviation of this random
In Exercise 11.118, we discuss the random variable counting the number of seniors in a sample of four undergraduate students at a university, given that the proportion of undergraduate students who
In Exercise 11.117, we discuss the random variable counting the number of girls in three babies, given that the proportion of babies who are girls is about 0.49. Find the mean and standard deviation
In the 2010 US Census, we learn that 65% of all housing units are owner-occupied while the rest are rented. If we take a random sample of 20 housing units, find the probability that:(a) Exactly 15 of
In the 2010 US Census, we learn that 13% of all people in the US are 65 years old or older. If we take a random sample of 10 people, what is the probability that 3 of them are 65 or older? That 4 of
From the 2010 US Census, we learn that 27.5% of US adults have graduated from college. If we take a random sample of 12 US adults, what is the probability that exactly 6 of them are college graduates?
Suppose that undergraduate students at a university are equally divided between the four class years (first-year, sophomore, junior, senior) so that the probability of a randomly chosen student being
Worldwide, the proportion of babies who are boys is about 0.51. A couple hopes to have three children and we assume that the sex of each child is independent of the others. Let the random variable X
A binomial random variable with n = 800 and p = 0.25Calculate the mean and standard deviation of the binomial random variable.
Abinomial random variable with n = 30 and p = 0.5Calculate the mean and standard deviation of the binomial random variable.
A binomial random variable with n = 10 and p = 0.8Calculate the mean and standard deviation of the binomial random variable.
A binomial random variable with n = 6 and p = 0.4Calculate the mean and standard deviation of the binomial random variable.
Find P(X = 8) if X is a binomial random variable with n = 12 and p = 0.75.Calculate the requested binomial probability.
Find P(X = 3) if X is a binomial random variable with n = 10 and p = 0.4.Calculate the requested binomial probability.
Find P(X = 7) if X is a binomial random variable with n = 8 and p = 0.9.Calculate the requested binomial probability.
Find P(X = 2) if X is a binomial random variable with n = 6 and p = 0.3.Calculate the requested binomial probability.
Calculate the requested quantity.
Calculate the requested quantity. (10)
Calculate the requested quantity. 2
Calculate the requested quantity. 8' 3,
Calculate the requested quantity.6!
Calculate the requested quantity.8!
Calculate the requested quantity.7!
Calculate the requested quantity.4!
Worldwide, the proportion of babies who are boys is about 0.51. We randomly sample 100 babies born and count the number of boys.Determine whether the process describes a binomial random variable. If
Suppose 30% of students at a large university take Intro Stats. Randomly sample 75 students from this university and count the number who have taken Intro Stats.Determine whether the process
Sample 50 students who have taken Intro Stats and record the final grade in the course for each.Determine whether the process describes a binomial random variable. If it is binomial, give values for
Roll a die until you get 5 sixes and count the number of rolls required.Determine whether the process describes a binomial random variable. If it is binomial, give values for n and p. If it is not
Count the number of sixes in 10 dice rolls.Determine whether the process describes a binomial random variable. If it is binomial, give values for n and p. If it is not binomial, state why not.
In a certain board game participants roll a standard six-sided die and need to hit a particular value to get to the finish line exactly. For example, if Carol is three spots from the finish, only a
Frank Benford, a physicist working in the 1930s, discovered an interesting fact about some sets of numbers. While you might expect the first digits of numbers such as street addresses or checkbook
An Internet Service Provider (ISP) offers its customers three options:• Basic: Standard internet for everyday needs, at $23.95 per month.• Premium: Fast internet speeds for streaming video and
A non-profit organization plans to offer a life insurance service. Participants agree to a five-year contract in which they pay the organization a yearly fee. The fee does not change over the course
As we see in Exercise 11.38 on page 653, during the 2010–11 NBA season, Ray Allen of the Boston Celtics had a free throw shooting percentage of 0.881. Assume that the probability Ray Allen makes
Refer to Table 11.14 in Exercise 11.88 that gives probabilities for the number of used cars a dealer sells in a day. What is the probability that the dealership sells no cars on three consecutive
Refer to Table 11.13 in Exercise 11.87 that gives probabilities for fruit fly lifetimes.Table 11.13(a) If we know a fruit fly died before the end of its second month, what is the probability it died
A used car dealership uses past data to estimate the probability distribution for the number of cars they sell in a day, X. The probability distribution of X is given inTable 11.14.(a) What is P(X =
Table 11.12 in Exercise 11.84 gives the probability function for the random variable giving the household size for a renter-occupied housing unit in the US.Table 11.12(a) Find the mean household
Table 11.12 gives the probability function for the random variable giving the household size for a renter-occupied housing unit in the US.Table 11.12(a) Verify that the sum of the probabilities is 1
Table 11.11 gives the probability function for the random variable giving the household size for an owneroccupied housing unit in the US. Table 11.11(a) Verify that the sum of the probabilities
Use the probability function given in the table to calculate:(a) The mean of the random variable(b) The standard deviation of the random variable 12 10 16 14 p(x) 0.25 0.25 0.25 0.25
Use the probability function given in the table to calculate:(a) The mean of the random variable(b) The standard deviation of the random variable х 20 30 40 50 0.1 p(x) 0.6 0.2 0.1
Use the probability function given in the table to calculate:(a) The mean of the random variable(b) The standard deviation of the random variable 2 3 х 0.5 p(x) 0.2 0.3
Fill in the ? to make p(x) a probability function. If not possible, say so. 3 4 х p(x) 0.3 ? 0.3 0.3 0.3
Fill in the ? to make p(x) a probability function. If not possible, say so. 2 3 ? p(x) 0.5 0.6

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