Stats chapter 5-7 Exam
Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X has a bell-shaped distribution with a mean of $360 and standard deviation of $50. What is the expected value and standard deviation, respectively, of the profits that the store makes in a seven-day period?
$2,520 and $132.29
There are 13 Democrats, 12 Republicans, and 8 Independents sitting in a room. Eight of these people will be selected to serve on a special committee. What is the probability that exactly five of the committee members will be Democrats?
.10783
Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes from 2 to 3 minutes to fill an order?
.1283
The telephone sales department of a certain store receives an average of 24 calls per hour. What is the probability that between 10:00 a.m. and 10:05 a.m. there will be 3 calls?
.1804
A department store has determined in connection with its inventory control that the demand for a certain CD player averages 4 per day. If the store stocks 5 of these items on a particular day, what is the probability that demand will exceed supply?
.2150
The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the probability that it takes more than 5 minutes to ring up a customer?
.2397
The height of the probability density function for a uniform distribution ranging between 2 and 6 is:
.25
A medicine is known to produce side effects for 1 in 5 patients taking it. Suppose a doctor prescribes the medicine to 4 unrelated patients. What is the probability that none of the patients will develop side effects?
.4096
For the standard normal probability distribution, the area to the left of the mean is:
.50
The random variable x is known to be uniformly distributed between 2 and 12. Compute P(x > 6).
.60
The primary air exchange system on a proposed spacecraft has four separate components (call them A, B, C, and D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = 0.95, P(B) = 0.90, P(C) = 0.99, and P(D) = 0.90. Find the probability that the entire system works properly.
.7618
Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X has a bell-shaped distribution with a mean of $360 and standard deviation of $50. What is the z-score that corresponds to the likelihood of the profit of $400?
.80
If the probability of a basketball player scoring on any shot is .75, what is the probability that she will score on at most 5 of her next 6 shots?
.8220
If z is a standard normal random variable, then compute P(z > -1.75).
.96
The primary air exchange system on a proposed spacecraft has four separate components (call them A, B, C, and D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = .95, P(B) = .90, P(C) = .99, and P(D) = .90. What is the probability that at least one of the four components will work properly?
.999995
The random variable x is known to be uniformly distributed between 2 and 12. Compute P(x = 6).
0
There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) that are possible is equal to:
15
The random variable x is known to be uniformly distributed between 2 and 12. Compute the standard deviation of x.
2.887
The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the standard deviation of this distribution?
3.5 min
A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n): exponential probability distribution. binomial probability distribution. uniform probability distribution. normal probability distribution.
A
A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. What is the probability that he takes less than 15,000 steps in a given day? .9996 1 .9770 .95
A
A normal distribution with a mean of zero and a standard deviation of one is called: a standard normal probability distribution. a uniform probability distribution. an ordinary normal curve. a probability density function.
A
A sample of 400 observations will be taken from an infinite population. The population proportion equals .8. The probability that the sample proportion will be greater than .83 is: .0668. .5668. .9332. .4332.
A
As the sample size increases, the: standard error of the mean decreases. standard error of the mean increases. population mean increases. standard deviation of the population decreases.
A
If z is a standard normal random variable, then compute P(-1.5 < z < 1.5). .87 1 .43 0
A
Roth is a computer-consulting firm. The number of new clients that the firm has obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. What is the expected number of new clients per month? 3.05 21 0 6
A
The U.S. Senate has 100 members. Suppose there are 54 Republicans and 46 Democrats. A committee of 15 senators is selected at random. What is the expected number of Republicans on this committee? 8.1 9.0 7.1 6.7
A
The central limit theorem is important in statistics because it: enables reasonably accurate probabilities to be determined for events involving the sample average when the sample size is large regardless of the distribution of the variable. tells us that if several samples have produced sample averages, which seem to be different than expected, the next sample average will likely be close to its expected value. guarantees that when it is applied, the samples that are drawn are always randomly selected. tells us that large samples do not need to be selected.
A
The distribution of values taken by a statistic in all possible samples of the same size from the same population is called a: sampling distribution. distribution of interest. population parameter. sample parameter.
A
The expected value for a binomial distribution is: np. np(1 − p). np(1 − np). np(n − 1).
A
The following represents the probability distribution for the daily demand of computers at a local store. What is the expected daily demand? 2.2 4.0 2.0 1.0
A
The random variable is the number of occurrences of an event over an interval of 10 minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. The appropriate probability distribution for the random variable is: discrete. continuous. either discrete or continuous depending on how the interval is defined. interval.
A
The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. Which of the following expressions gives the probability that it takes from 1 to 2 minutes to ring up a customer?
A
There is a lower limit but no upper limit for a random variable that follows the: exponential probability distribution. binomial probability distribution. normal probability distribution. uniform probability distribution.
A
Which of the following is a point estimator? s p μ σ
A
Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable? The trials are dependent upon one another. The probabilities of the outcomes do not change from one trial to another. There are exactly two outcomes are possible on each trial. The experiment has a sequence of identical trials.
A
Which of these best describes a sampling distribution of a statistic? It is the distribution of all of the statistics calculated from all possible samples of the same sample size. It is the histogram of sample statistics from all possible samples of the same sample size. It is the probability distribution of the values of a statistic that are contained in all possible samples of the same sample size. It is the probability that the sample statistic equals the parameter of interest.
A
A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution? 10,000 12,467 8078 7533
B
A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let x = the number of puzzles completed successfully by a subject. The psychologist found that x had the following probability distribution: What is the mean number of puzzles the subjects can be expected to complete? 2.2 2.3 2.0 1.0
B
A sample of 66 observations will be taken from an infinite population. The population proportion equals .12. The probability that the sample proportion will be less than .1768 is: .42. .92. .08. .06.
B
A simple random sample of 64 observations was taken from a large population. The sample mean and standard deviation were determined to be 320 and 120, respectively. The standard error of the mean is: 5. 15. 40. 1.875.
B
An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is 0.2 and having a major accident is 0.05, how much can the insurance company expect to make on the policy? (Expected profit) $300 $350 $250 $200
B
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when: np ≥ 5. n(1 - p) ≥ 5 and np ≥ 5. n ≥ 30 and n(1 - p) = 5. np ≤ 5.
B
How many simple random samples of size 5 can be selected from a population of size 8? 336 56 68 40
B
If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow a(n): uniform probability distribution. exponential probability distribution. normal probability distribution. Poisson probability distribution.
B
Random variable x has the following probability function: What is the expected value of x ? 2.00 2.33 .50 .33
B
Suppose that a basketball player scored, on average, 15 points per game. Also suppose that the distribution of points scored by this player was normal. If he scores 20 points or more 4.78% of the time, what is his standard deviation? 2.5 3 2 1.5
B
The probability distribution of all possible values of the sample proportion is the: same as , since it considers all possible values of the sample proportion. sampling distribution of . sampling distribution of . probability density function of .
B
The random variable x is known to be uniformly distributed between 2 and 12. Compute P(x ≥ 6). .50 .60 .40 0
B
The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the variance of this distribution? 7 minutes 12.25 minutes 3.5 minutes 1.87 minutes
B
The value of the _____ is used to estimate the value of the population parameter. population estimate sample statistic sample parameter population statistic
B
The variance Var(x) for the binomial distribution is: n(1 − p). np(1 − p). np(1 − np). np(n − 1).
B
We cannot select a simple random sample from an infinite population because: each element selected comes from a different population. we cannot construct a frame consisting of all the elements. it would take an unreasonable amount of time. each element is selected dependently.
B
Which of the following is a nonprobability sampling technique? Cluster sampling Judgment sampling Stratified random sampling Simple random sampling
B
Which one of these variables is a continuous random variable? The number of women taller than 68 inches in a random sample of five women The time it takes a randomly selected student to complete an exam The number of tattoos a randomly selected person has The number of correct guesses on part A of the multiple choice test
B
A bookstore is interested in genre and author preferences. They form a panel by taking the first 10 people who volunteer while walking by their storefront. They then conduct a brief interview and compile their results. This is an example of: systematic sampling stratified random sampling convenience sampling judgement sampling
C
A negative value of z indicates that: a mistake has been made in computations, since z cannot be negative. the data has a negative mean. the number of standard deviations of an observation is below the mean. the number of standard deviations of an observation is above the mean.
C
An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a: complex random variable. categorical random variable. continuous random variable. discrete random variable.
C
Cluster sampling is: a nonprobability sampling method. the same as convenience sampling. a probability sampling method. a form of systematic sampling.
C
Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order? .6321 .7769 .4866 .1813
C
Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the variance of this distribution? 3 minutes 0.75 minutes 2.25 minutes 1.5 minutes
C
For a(n) _____ , it is impossible to construct a sampling frame. target population defined population infinite population finite population Feedback: Incorrect. For an infinite population, it is impossible to construct a sampling frame. See Section 7.1, The Electronics Associates Sampling Problem.
C
In a standard normal distribution, what z-score corresponds to the 75th percentile? z = .75 z = 1.75 z = .67 z = .07
C
Parameters are: the averages taken from a sample. numerical characteristics of either a sample or a population. numerical characteristics of a population. numerical characteristics of a sample.
C
Roth is a computer-consulting firm. The number of new clients that the firm has obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. What is the variance of the number of new clients? 3.05 21 2.048 1.431
C
The Poisson probability distribution is a: uniform probability distribution. normal probability distribution. discrete probability distribution. continuous probability distribution.
C
The binomial probability distribution is used with: a uniform random variable. an intermittent random variable. a discrete random variable. a continuous random variable.
C
The sample statistic characteristic s is the point estimator of: ρ. π. σ. μ.
C
The sampling distribution of is the: mean of the sample. mean of the population. probability distribution of all possible values of the sample proportion. probability distribution of all possible values of the sample mean.
C
What is the mean of x, given the exponential probability function for x ≥ 0? 100 2000 20 .05
C
When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a: normal distribution. hypergeometric probability distribution. Poisson distribution. binomial distribution.
C
Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable? The trials are dependent upon one another. The probabilities of the outcomes changes from one trial. There are exactly two outcomes possible on each trial. The experiment has at least two possible outcomes.
C
Which of the following is not true of discrete probability distributions? The value of the standard deviation can be less than, equal to, or greater than the value of the mean. Each of the probability in the distribution must be greater than or equal to 0. The graph of the distribution always exhibits symmetry. The sum of the probabilities is 1.
C
A continuous random variable may assume: only fractional values in an interval or collection of intervals. only the positive integer values in an interval. only integer values in an interval or collection of intervals. any numerical value in an interval or collection of intervals.
D
A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. What percent of the time will he exceed 13,000 steps? 95% 97.72% 5.0% 2.28%
D
Doubling the size of the sample will: have no effect on the standard error of the mean. double the standard error of the mean. increase the standard error of the mean. reduce the standard error of the mean.
D
Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the standard deviation of this distribution? 3 minutes 0.75 minutes 2.25 minutes 1.5 minutes
D
Find the probability that a family of five children will have exactly three boys. .8125 .1875 .6875 .3125
D
Sample statistics, such as x̅ , s, or p̅, that provide the point estimate of the population parameter are known as: target population. population statistics. parameter values. point estimators.
D
The average annual incomes of high school and college graduates in a midwestern town are $21,000 and $35,000, respectively. If a company hires only personnel with at least a high school diploma and 20% of its employees have been through college, what is the mean income of the company employees? $28,000 $32,200 $27,110 $23,800
D
The distribution of values taken by a statistic in all possible samples of the same size from the same population is the sampling distribution of: the distribution. the target population. the population. the sample.
D
The drying time of one particular paint is approximately normally distributed with a mean of 45 minutes. It is also known that 15% of walls painted with this paint need more than 55 minutes to dry completely. Find the standard deviation of this distribution. σ=9.82 σ=9.92 σ=9.72 σ=9.62
D
The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50th percentile of this distribution? 95 105 85 75
D
Which of the following is(are) true? I. The mean of a population depends on the particular sample chosen.II. The standard deviations of two different samples from the same population may be the same.III. Statistical inferences can be used to draw conclusions about the populations based on sample data.
II and III
In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that models this situation is the:
Poisson distribution
The random variable is the number of occurrences of an event over an interval of 10 minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. The random variable satisfies the:
Poisson probability distribution.
Which of the following is a discrete random variable?
The number of times a student guesses the answers to questions on a certain test
Which of the following is not a characteristic of the normal probability distribution?
The standard deviation must be one.
Which of the following statements regarding the sampling distribution of sample means is incorrect?
The standard deviation of the sampling distribution is the standard deviation of the population.
The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is:
a parameter.
A discrete uniform probability distribution is one where _______.
each possible value of the random variable is the same
Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their orders at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order?
f(x)=2/3e '-2/3x'
The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the probability density function for the time it takes to ring up a customer?
f(x)=2/7e'-2/7x'
A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size:
n has the same probability of being selected
Convenience sampling is a:
nonprobability sampling technique.
A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately normal because
of the central limit theorem.
Which of the following is not a symbol for a parameter?
s
The standard deviation of a point estimator is called the:
standard error.
The center of a normal curve is:
the mean of the distribution
A random sample of 12 four-year-old red pine trees was selected and the diameter (in inches) of each tree's main stem was measured. The resulting observations are as follows: 11.3, 10.7, 12.4, 15.2, 10.1, 12.1 , 16.2, 10.5, 11.4, 11.0, 10.7, and 12.0 Find the point estimate that can be used to estimate the true population mean.
x̅ = 11.97
