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Q:
The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.
A. normal
B. exponential
C. Poisson
D. binomial
E. uniform
Q:
A property of continuous distributions is that
A. as with discrete random variables, the probability distribution can be approximated by a smooth curve.
B. probabilities for continuous variables can be approximated using discrete random variables.
C. unlike discrete random variables, probabilities can be found using tables.
D. unlike discrete random variables, the probability that a continuous random variable equals a specific value is zero [P(X = x) = 0].
Q:
A standard normal distribution has a mean of ____________ and standard deviation of ____________.
A. zero, zero
B. zero, one
C. one, one
D. one, zero
Q:
The mean life of a pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?
A. 500,000
B. 808,500
C. 191,500
D. 308,500
Q:
The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x)?
A. 0
B. 1
C. 1/6
D. 1/14
Q:
It is appropriate to use the uniform distribution to describe a continuous random variable x when
A. the area under the probability curve = 1.
B. the probability curve f(x) > 0.
C. the shape of the histogram of all possible values of x is nonsymmetrical.
D. relative frequencies of all possible values of x are about the same.
Q:
In order to approximate the binomial distribution using the normal distribution, the following condition(s) must be met if p is near 1.
A. np > 5 only
B. n must be larger than just meeting the condition of np > 5.
C. n can be as small as np > 5.
D. n > 5
Q:
The first step to constructing a normal probability plot is to
A. calculate Oi.
B. compute area i/(n + 1).
C. construct a box-and-whiskers plot.
D. order the values in the data.
Q:
The ___________ is a graphic that is used to check visually whether data come from a normal population.
A. exponential plot
B. normal probability plot
C. box-and-whiskers plot
D. normal distribution graph
Q:
The standardized normal quantile value Oi is the z value that gives an area of i/(n -1) to its right under the normal curve.
Q:
If the distances between the ordered data values are proportional to the distances between the actual values, then the normal probability plot will be a straight line.
Q:
For a binomial probability experiment, with n = 150 and p = .2, it is appropriate to use the normal approximation to the binomial distribution.
Q:
If the random variable x is normally distributed, 68.26 percent of all possible observed values of x will be within two standard deviations of the mean.
Q:
The z value tells us the number of standard deviations that a value x is from the mean.
Q:
A continuous random variable may assume only integer values in a given interval.
Q:
The normal probability distribution is a discrete probability distribution.
Q:
The standard deviation of a standard normal distribution is always equal to 1.
Q:
The mean of a standard normal distribution is always equal to 1.
Q:
The exponential probability distribution is based on a continuous random variable.
Q:
A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers, is called a uniform probability distribution.
Q:
For a continuous random variable x, the height of the probability curve f(x) at a particular point indicates the value of the probability for that value.
Q:
For a continuous distribution, the exact probability of a particular value is zero.
Q:
All continuous random variables are normally distributed.
Q:
For a continuous distribution, P(X 100) = P(X < 100).
Q:
The number of defective pencils in a lot of 1000 is an example of a continuous random variable.
Q:
The actual weight of hamburger patties is an example of a continuous random variable.
Q:
In a statistical study, the random variable X = 1 if the house is colonial, and X = 0 if the house is not colonial. The random variable X is continuous.
Q:
The mean and median are the same for an exponential distribution.
Q:
The mean and median are the same for a normal distribution.
Q:
A uniform distribution f(x) is a continuous probability distribution, which says the probability that x is in any 2 intervals of equal length is the same.
Q:
The local airport in a Midwestern state keeps track of the percentage of flights arriving within 15 minutes of their scheduled arrivals. The stem-and-leaf plot of the data for one year is below. Construct a normal probability plot and interpret the plot.
Q:
The local airport in a Midwestern state keeps track of the percentage of flights arriving within 15 minutes of their scheduled arrivals. The stem-and-leaf plot of the data for one year is below.Compute the standardized quantile value Oi for i = 11.
Q:
A local airport in a midwestern state keeps track of the percentage of flights arriving within 15 minutes of their scheduled arrivals. The stem-and-leaf plot of the data for one year is below. Compute the standardized quantile value Oi for i = 4.
Q:
The binomial random variable x consists of n = 60 trials and has the probability of failure q = 0.4. Using the normal approximation, compute the probability of 45 successes.
Q:
The binomial random variable x consists of n = 60 trials and has the probability of failure q = 0.4. Using the normal approximation, compute the probability of 19 successes.
Q:
The binomial random variable x consists of n = 60 trials and has the probability of failure q = 0.4. Using the normal approximation, compute the probability of 32 successes.
Q:
The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time is between 2 and 4 minutes?
A. .2488
B. .4493
C. .2019
D. .2474
E. .1170
Q:
The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time is no more than 3 minutes?
A. .3012
B. .6988
C. .4346
D. .5654
E. .0821
Q:
The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time exceeds 3 minutes?
A. .3012
B. .6988
C. .4346
D. .5654
E. .0821
Q:
Suppose the distribution of personal daily water usage in New York City is normally distributed with a mean of 15 gallons and a variance of 25 gallons. Because of a current problem with the distribution of water to its citizens, the mayor wants to give a city tax rebate to the 15 percent of the population who use the least amount of water. What should he use as the water limit for a person to qualify for a city tax rebate?
A. 9.825
B. 15.00
C. 12.20
D. 10.25
Q:
A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes of supplies that arrive be greater than 210 or less than 180?
A. 69.15%
B. 46.72%
C. 19.15%
D. 15.87%
Q:
A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will between 180 and 210 boxes of supplies arrive in a week?
A. 69.15%
B. 19.15%
C. 53.28%
D. 15.87%
Q:
A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will fewer than 160 boxes of supplies arrive in a week?
A. 2.28%
B. 57.93%
C. 42.07%
D. 4.56%
Q:
A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received in a week exceed 200?
A. 100%
B. 25%
C. 0%
D. 50%
Q:
Find z when the area to the left of z is .05.A. 1.645B. 1.00C. -1.645D. -1.96
Q:
Find z when the area between z and -z is .9030.A. 1.50B. 1.30C. 0.12D. 1.66
Q:
Find z when the area to the left of z is .6700.A. 0.75B. 0.44C. -0.44D. -0.75
Q:
Find z when the area to the right of z is .1314.A. 1.12B. 0.55C. -0.55D. -1.12
Q:
Find z when the area between 0 and z is .4750.A. -1.96B. 1.96C. 0.68D. -0.68
Q:
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. Between what two values (in ounces) symmetrically distributed around the population mean will 80 percent of the apples fall?
A. [2.13, 2.37]
B. [2.10, 2.40]
C. [2.06, 2.44]
D. [1.95, 2.55]
Q:
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. 77 percent of the apples will contain at least how many ounces of juice?
A. 2.12
B. 2.38
C. 2.36
D. 2.14
Q:
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain more than 2.50 ounces?
A. .9525
B. .4525
C. .0475
D. .5474
Q:
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 2.50 ounces?
A. .500
B. .905
C. .9525
D. .9544
Q:
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces?
A. .0475
B. .4525
C. .9525
D. .9554
Q:
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is within 1 standard deviation of the mean?
A. 0.320
B. 0.576
C. 0.600
D. 1.000
Q:
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the standard deviation of the water depth?
A. 1.4
B. 2.6
C. 2.5
D. 4.5
Q:
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the expected value of the water depth?
A. 1.4
B. 2.6
C. 2.5
D. 4.5
Q:
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?
A. .79
B. .45
C. .55
D. .50
Q:
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is less than 3.60 m?
A. .72
B. .80
C. .46
D. .32
Q:
A manufacturer of personal computers tests competing brands and finds that the amount of energy they require is normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. If the lowest 25 percent and the highest 30 percent are not included in a second round of tests, what are the upper and lower limits for the energy amounts of the remaining computers?
A. [269.76, 300.24]
B. [278.86, 289.78]
C. [280.22, 289.78]
D. [280.22, 300.24]
Q:
A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. Only 5 percent of the students taking the test scored higher than what grade?
A. 70.04
B. 67.96
C. 55.48
D. 82.52
Q:
A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What proportion of students scored between 81 and 89?
A. .0668
B. .0132
C. .0786
D. .0529
Q:
A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What percentage of students scored between 65 and 89?
A. 65.68%
B. 100%
C. 98.68%
D. 33.00%
Q:
A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What is the probability of getting a grade of 91 or less on this exam?
A. 1.00
B. 0.50
C. 0.0073
D. .9927
Q:
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Complete the following statement: Only 20 percent of the individuals wait less than _____ minutes.
A. 36.72
B. 23.28
C. 34.63
D. 25.37
Q:
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?
A. 34.48
B. 21.68
C. 38.32
D. 25.52
Q:
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time of no more than 22 minutes?
A. .1587
B. .9977
C. .8413
D. .0023
Q:
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time of at least 10 minutes?
A. .9938
B. .8944
C. .1056
D. .0062
Q:
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes?
A. 1.00
B. .9699
C. .5000
D. .9398
Q:
Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean?
A. 0.75
B. 1.00
C. 0.58
D. 0.86
Q:
Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit will take at least 50 minutes?
A. .77
B. .40
C. .60
D. .23
Q:
During the past six months, 73.2 percent of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. 80 percent of the households spent more than what amount?
A. $7.30
B. $7.38
C. $9.06
D. $9.14
Q:
During the past six months, 73.2 percent of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. 99 percent of the households spent less than what amount?
A. $5.66
B. $10.78
C. $6.81
D. $9.63
Q:
During the past six months, 73.2 percent of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. What proportion of the households spent between $5.00 and $9.00 on sugar?
A. .7611
B. .7628
C. .0017
D. .7594
Q:
During the past six months, 73.2 percent of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent more than $16.00 on sugar.
A. 1.00
B. 0.00
C. 0.50
D. 0.98
Q:
During the past six months, 73.2 percent of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent more than $10.00 on sugar.
A. .7320
B. .9474
C. .0526
D. .2680
Q:
During the past six months, 73.2 percent of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent less than $5.00 on sugar.
A. .9983
B. 0.000
C. 1.00
D. 0.0017
Q:
At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25 C. What is the standard deviation of the temperature increase?
A. 10.12
B. 4.33
C. 7.50
D. 1.25
Q:
At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25 C. What is the expected value of the temperature increase?
A. 7.50
B. 4.33
C. 17.50
D. 10.12
Q:
At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25 C.
Suppose that a temperature increase of more than 18 C is considered to be potentially dangerous to the environment. What is the probability that at any point in time, the temperature increase is potentially dangerous?
A. 0.47
B. 0.72
C. 0.28
D. 0.50