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mathematics
statistics
Elementary Statistics A Step By Step Approach 8th Edition Allan Bluman - Solutions
A shipment of 24 computer keyboards is rejected if 4 are checked for defects and at least 1 is found to be defective. Find the probability that the shipment will be returned if there are actually 6 defective keyboards.
A shipment of 24 electric typewriters is rejected if 3 are checked for defects and at least 1 is found to be defective. Find the probability that the shipment will be returned if there are actually 6 typewriters that are defective.
According to the manufacturer, M&M’s are produced and distributed inthe following proportions: 13% brown, 13% red, 14% yellow, 16% green, 20% orange, and 24% blue. In a random sample of 12 M&M’s, what is the probability of having 2 of each color?
Find each probability P(X; l), using Table C in Appendix C.a. P (5; 4)b. P (2; 4)c. P (6; 3)d. P (10; 7)e. P (9; 8)
A recent study of robberies for a certain geographic region showed an average of 1 robbery per 20,000 people. In a city of 80,000 people, find the probability of the following.a. 0 robberies b. 1 robbery c. 2 robberies d. 3 or more robberies
During a recent paint sale at Corner Hardware, the number of cans of paint purchased was distributed as shown. Find the mean, variance, and standard deviation of the distribution.
The number of inquiries received per day for a college catalog is distributed as shown. Find the mean, variance, and standard deviation for the data.
A game is set up as follows: All the diamonds are removed from a deck of cards, and these 13 cards are placed in a bag. The cards are mixed up, and then one card is chosen at random (and then replaced). The player wins according to the following rules.If the ace is drawn, the player loses $20. If a
Using Exercise 13, how much should be charged if instead of winning $2 for drawing a 2–10, the player wins the amount shown on the card in dollars?Reference Exercise:Card Game A game is set up as follows: All the diamonds are removed from a deck of cards, and these 13 cards are placed in a bag.
Let x be a binomial random variable with n = 12 and P = 0.3. Find the following:a. P(X = 8) b. P(X < 5) c. P(X ≤ 10) d. P (4 < X ≤ 9) (5 – 3)
It has been reported that 63% of adults aged 65 and over got their flu shots last year. In a random sample of 300 adults aged 65 and over, find the mean, variance, and standard deviation for the number who got their flu shots.
The chance that a U.S. police chief believes the death penalty “significantly reduces the number of homicides” is 1 in 4. If a random sample of 8 police chiefs is selected, find the probability that at most 3 believe that the death penalty significantly reduces the number of homicides.
Computer Help Hot Line receives, on average, 6 calls per hour asking for assistance. The distribution is Poisson. For any randomly selected hour, find the probability that the company will receive a. At least 6 calls b. 4 or more calls c. At most 5 calls
The number of emergency calls a local police department receives per 24-hour period is distributed as shown here. Construct a graph for the data.
A large retail company encourages its employees to get customers to apply for the store credit card. Below is the distribution for the number of credit card applications received per employee for an 8-hour shift.a. What is the probability that an employee will get 2 or 3 applications during any
A box contains 5 pennies, 3 dimes, 1 quarter, and 1 half-dollar. Construct a probability distribution and draw a graph for the data.
At Tylers Tie Shop, Tyler found the probabilities that a customer will buy 0, 1, 2, 3, or 4 ties, as shown. Construct a graph for the distribution.
A bank has a drive-through service. The number of customers arriving during a 15-minute period is distributed as shown. Find the mean, variance, and standard deviation for the distribution.
At a small rural airport, the number of arrivals per hour during the day has the distribution shown. Find the mean, variance, and standard deviation for the data.
What are the characteristics of a normal distribution?
To the right of z = 2.01 0.0222 Find the area under the standard normal distribution curve.
To the right of z = 0.29 Find the area under the standard normal distribution curve.
To the left of z = –0.75 Find the area under the standard normal distribution curve.
To the left of z = –1.39 Find the area under the standard normal distribution curve.
Between z = 1.23 and z = 1.90 Find the area under the standard normal distribution curve.
Between z = 1.05 and z = 1.78 Find the area under the standard normal distribution curve.
Between z = 0.96 and z = –0.36 Find the area under the standard normal distribution curve.
Between z = 1.56 and z = –1.83 Find the area under the standard normal distribution curve.
Between z = 0.24 and z = –1.12 Find the area under the standard normal distribution curve.
Between z = –1.46 and z = – 1.98 Find the area under the standard normal distribution curve.
To the left of z = 1.31 Find the area under the standard normal distribution curve.
To the left of z = 2.11 Find the area under the standard normal distribution curve.
To the right of z = –1.92 Find the area under the standard normal distribution curve.
To the right of z = – 0.17 Find the area under the standard normal distribution curve.
To the left of z = – 2.15 and to the right of z = 1.62 Find the area under the standard normal distribution curve.
To the right of z = 1.92 and to the left of z = –0.44 Find the area under the standard normal distribution curve.
Find the probabilities for each, using the standard normal distribution.P (0 < z < 1.96)
P (0 < z < 0.67)Find the probabilities for each, using the standard normal distribution.
P (– 1.23 < z < 0) Find the probabilities for each, using the standard normal distribution.
P (– 1.43 < z < 0) Find the probabilities for each, using the standard normal distribution.
P (z < 0.82) Find the probabilities for each, using the standard normal distribution.
P (z > 2.83) Find the probabilities for each, using the standard normal distribution.
P (z < – 1.77) Find the probabilities for each, using the standard normal distribution.
P (z < –1.32) Find the probabilities for each, using the standard normal distribution.
P (– 0.20 < z
P (– 2.46 < z
P (1.12< z < 1.43) Find the probabilities for each, using the standard normal distribution.
P (1.46< z < 2.97) Find the probabilities for each, using the standard normal distribution.
P (z > –1.43)Find the probabilities for each, using the standard normal distribution.
P (z < 1.42)Find the probabilities for each, using the standard normal distribution.
Find the z value that corresponds to the given area.
Find the z value to the right of the mean so thata. 54.78% of the area under the distribution curve lies to the left of it.b. 69.85% of the area under the distribution curve lies to the left of it. c. 88.10% of the area under the distribution curve lies to the left of it.
Find the z value to the left of the mean so thata. 98.87% of the area under the distribution curve lies to the right of it. b. 82.12% of the area under the distribution curve lies to the right of it.c. 60.64% of the area under the distribution curve lies to the right of it.
Find two z values so that 48% of the middle area is bounded by them.
Find two z values, one positive and one negative, that are equidistant from the mean so that the areas in the two tails total the following values.a. 5% b. 10% c. 1%
In the standard normal distribution, find the values of z for the 75th, 80th, and 92nd percentiles.
Find P (– 1 < z
Find z0 such that P ( – 1.2 < z < z0) = 0.8671.
Find z0 such that P (z0 < z < 2.5) = 0.7672.
Find z0 such that the area between z0 and z = –0.5 is 0.2345 (two answers).
Find z0 such that P (– z0 < z < z0) = 0.76.
Graph by hand the standard normal distribution by using the formula derived in Exercise 57. Let π ≈ 3.14 and e ≈ 2.718. Use X values of – 2, – 1.5, – 1, – 0.5, 0, 0.5, 1, 1.5, and 2. (Use a calculator to compute the y values.)
Between z = 0 and z = 1.77 Find the area under the standard normal distribution curve.
Between z = 0 and z = 0.75Find the area under the standard normal distribution curve.
Between z = 0 and z = –0.32 Find the area under the standard normal distribution curve.
Between z = 0 and z = – 2.07 Find the area under the standard normal distribution curve.
The average teacher’s salary in Connecticut (ranked first among states) is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500.a. What is the probability that a randomly selected teacher makes less than $52,000 per year? 0.2389b. If we sample 100
The mean serum cholesterol level of a large population of overweight children is 220 milligrams per deciliter (mg/dl), and the standard deviation is 16.3 mg/dl. If a random sample of 35 overweight children is selected, find the probability that the mean will be between 220 and 222 mg/dl. Assume the
The average teacher’s salary in North Dakota is $37,764. Assume a normal distribution with σ = $5100. a. What is the probability that a randomly selected teacher’s salary is greater than $45,000? b. For a sample of 75 teachers, what is the probability that the sample mean is greater
The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 mpg. If the standard deviation of the population was 2.9 and the gas ratings were normally distributed, what is the probability that the mean mpg for a random sample of 25 light
The national average SAT score (for Verbal and Math) is 1028. Suppose that nothing is known about the shape of the distribution and that the standard deviation is 100. If a random sample of 200 scores were selected and the sample mean were calculated to be 1050, would you be surprised? Explain.
The average number of milligrams (mg) of sodium in a certain brand of low-salt microwave frozen dinners is 660 mg, and the standard deviation is 35 mg. Assume the variable is normally distributed.a. If a single dinner is selected, find the probability that the sodium content will be more than 670
A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a
The Old Farmer’s Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. If the benefits are normally distributed with a standard deviation of $460, find the probability that the mean benefit for a random sample of 20 patients isa. Less than $3800 b. More than $4100
Procter & Gamble reported that an American family of four washes an average of 1 ton (2000 pounds) of clothes each year. If the standard deviation of the distribution is 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980
In a recent year, Delaware had the highest per capita annual income with $51,803. If σ = $4850, what is the probability that a random sample of 34 state residents had a mean income greater than $50,000? Less than $48,000?
The average annual precipitation for a large Midwest City is 30.85 inches with a standard deviation of 3.6 inches. Assume the variable is normally distributed.a. Find the probability that a randomly selected month will have less than 30 inches. b. Find the probability that the mean of a random
Assume that the mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed.a. If an individual is selected, find the probability that the individual’s pressure will be between 120 and 121.8 mm
The average cholesterol content of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.a. If a single egg is selected, find the probability that the cholesterol content will be greater than 220 milligrams. b. If a
At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard deviation is 3.7 years. Assume the variable is normally distributed.a. If a proofreader from the company is randomly selected, find the probability that his or her age will be between 36 and 37.5 yearb. If a
The average weekly income of information workers in private industry is $777. If the standard deviation is $77, what is the probability that a random sample of 50 information workers will earn, on average, more than $800 per week? Do we need to assume a normal distribution? Explain.
In a study of the life expectancy of 500 people in a certain geographic region, the mean age at death was 72.0 years, and the standard deviation was 5.3 years. If a sample of 50 people from this region is selected, find the probability that the mean life expectancy will be less than 70 years. Check
Astudy of 800 homeowners in a certain area showed that the average value of the homes was $82,000, and the standard deviation was $5000. If 50 homes are for sale, find the probability that the mean of the values of these homes is greater than $83,500. Check to see whether the correction factor
The average breaking strength of a certain brand of steel cable is2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population. Assume the variable is
The standard deviation of a variable is 15. If a sample of 100 individuals is selected, compute the standard error of the mean. What size sample is necessary to double the standard error of the mean?
In Exercise 29, what size sample is needed to cut the standard error of the mean in half?
Glass Garbage Generation Asurvey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds.
The mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for a recent academic year. Suppose that s$3204 and that 36 four-year institutions are randomly selected. Find the probability that the sample mean cost for these 36 schools isa. Less than $25,000
The average early-bird special admission price for a movie is $5.81. If the distribution of movie admission charges is approximately normal with a standard deviation of $0.81, what is the probability that a randomly selected admission charge is less than $3.50?
The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume that commuting times are normally distributed and that the standard deviation is 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes
The average credit card debt for college seniors is $3262. If the debt is normally distributed with a standard deviation of $1100, find these probabilities. a. That the senior owes at least $1000 b. That the senior owes more than $4000 c. That the senior owes between $3000 and $4000
The average retail price of gasoline (all types) for the first half of 2009 was 236.5 cents. What would the standard deviation have to be in order for a 15% probability that a gallon of gas costs less than $2.00?
The average waiting time at a drive-in window of a local bank is 10.3 minutes, with a standard deviation of 2.7 minutes. Assume the variable is normally distributed. If a customer arrives at the bank, find the probability that the customer will have to waita. Between 4 and 9 minutes b. Less than 5
Newborn elephant calves usually weigh between 200 and 250 pounds—until October 2006, that is. An Asian elephant at the Houston (Texas) Zoo gave birth to a male calf weighing in at a whopping 384 pounds! Mack (like the truck) is believed to be the heaviest elephant calf ever born at a facility
The average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes, with a standard deviation of 3.6 minutes. Assume the variable is normally distributed. When a patron arrives at the restaurant for dinner, find the probability that the patron will have to wait the following
The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of institution, the salary is $90,330. If the standard deviation for the salaries of both genders is approximately $5200 and
During September, the average temperature in Keystone Lake is 71.2°, and the standard deviation is 3.4°. For a randomly selected day, find the probability that the temperature of the lake is less than 63°. Based on your answer, would this be a likely or unlikely occurrence? Assume the variable
The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 50% of contributions.
A contractor decided to build homes that will include the middle 80% of the market. If the average size of homes built is 1810 square feet, find the maximum and minimum sizes of the homes the contractor should build. Assume that the standard deviation is 92 square feet and the variable is normally
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