Statistics wiggity

Suppose candidate A for a town council seat receives 43% of the votes in an election. As voters leave the polls they are asked who they voted for. What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A? Assume an infinite population. a. .2939 b. .7061 c. .1368 d. .8632

a. .2939

A population of size 320 has a proportion equal to .60 for the characteristic of interest. What are the mean and the standard deviation, respectively, of the sample proportion for samples of size 12? a. .60 and.14 b. 192 and 45 c. .60 and.02 d. 320 and.02

a. .60 and.14

The time it takes to completely clean an office building follows an exponential distribution with a mean of 135 minutes. What is the probability of cleaning an office building in 135 minutes or less? a. .6321 b. .50 c. .3679 d. 1.00

a. .6321

A local retailer received a shipment of 20 items that included 6 defective and 14 nondefective items. In the inspection of the shipment, a sample of 8 items will be selected and tested. The mean number of defective items is: a. 2.4 b. 5.6 c. .3 d. 6

a. 2.4

Suppose a preliminary screening is given to prospective student athletes at a university to determine whether they would qualify for a scholarship. The scores are approximately normal with a mean of 85 and a standard deviation of 20. If the range of possible scores is 0 to 100, what percentage of students has a score less than 85? a. 50% b. 100% c. 8.5% d. 98.34%

a. 50%

The sampling distribution describes the: a. sample size. b. long-run behavior of a statistic. c. short-term behavior of the population. d. population proportion.

b. long-run behavior of a statistic.

The variance is a weighted average of the: a. squared deviations from the median b. square root of the deviations from the mean c. squared deviations from the mean d. square root of the deviations from the median

c. squared deviations from the mean

Suppose that the lifetime of batteries in a flashlight is exponentially distributed with a mean of 35 hours. What is the probability that the batteries will last between 25 and 30 hours? a. .5105 b. .5756 c. .4244 d. .0651

d. .0651

Using a hypergeometric distribution with N = 6 and r = 2, what is the probability for n = 4 and x = 0? a. .0001 b. .9333 c. .6667 d. .0667

d. .0667

What is the mean of x for the exponential distribution, f(x)=(1/2)e^-x/2, x ≥ 0? a. 1.36 b. 0 c. .5 d. 2

d. 2

If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, which of the following probabilities is not correct? a. P(x ≤ 1) =.8413 b. P(x < 2) =.9772 c. P(x ≥ 1) =.1587 d. P(x = 0) =.50

d. P(x = 0) =.50

A simple random sample of size 5 from an infinite population is to be selected. Each possible sample should have: a. a probability of .2 of being selected. b. a different probability of being selected. c. a probability of .5 of being selected. d. the same probability of being selected.

d. the same probability of being selected.

Which of the following is an unbiased point estimator? a. n is an unbiased estimator of x̄ b. s is an unbiased estimator of sigma c. All of these choices are correct. d. x̄ is an unbiased estimator of μ

d. x̄ is an unbiased estimator of μ

The population mean is represented by the symbol: a.x̄ b. sigma c. S d. μ

d. μ

Let x be a uniform random variable on the interval 1≤x≤6. What is the standard deviation of x? a. 1.44 b. 2.08 c. .2 d. 3.5

?

When the selection of one element from the population influences the selection of another element, the sample: a. was selected using computer-generated random numbers. b. contains selection bias. c. is from a finite population. d. is a simple random sample.

b. contains selection bias.

The symbol p typically represents a: a. mean. b. proportion. c. standard deviation. d. sample size.

b. proportion.

A production process produces 2% defective parts. A sample of nine parts from the production process is selected. What is the probability that the sample contains exactly two defective parts? a. .0200 b. .9994 c. .0125 d. .9875

c. .0125

A small business owner determines that her revenue during the next year should be approximately normally distributed with a mean of $425,000 and a standard deviation of $130,000. What is the probability that her revenue will exceed $600,000? a. .9999 b. .5000 c. .0885 d. .9115

c. .0885

An air traffic controller has noted that it clears an average of 7 planes per hour for landing. What is the probability that during the next two hours exactly 15 planes will be cleared for landing? a. .0651 b. .0033 c. .0989 d. Not enough information is given to answer the problem.

c. .0989

Consider the continuous random variable x, which has a uniform distribution over the interval from 110 to 150. The probability that x will take on a value between 120 and 125 is: a. .025 b. .50 c. .125 d. .20

c. .125

Let x be a Poisson random variable with mean = 3. What is f(2)? a. 1.732 b. .1804 c. .2240 d. .4232

c. .2240

The probability function for the number of people in a randomly selected vehicle is given below. What is the probability that there are less than three people in a randomly selected vehicle? x |1 | 2 | 3 | 4 f(x)|.4|.35|.15|.1 a. .25 b. .90 c. .75 d. 1

c. .75

A production line fills 64 ounce bottles of juice uniformly according to the following probability density function. F(x)={4 for 63.85≤64.10} {0 elsewhere} What is the probability that the bottle will be filled between 63.90 and 64 ounces? a. .25 b. .50 c. .16 d. .4

d. .4

A random sample of 150 individuals who purchased a computer was taken. The survey determined that 70 of the individuals purchased Brand D. Which of the following is an unbiased estimate of the population proportion of all computers purchased that are Brand D? a. .53 b. 70 c. The population proportion is not known so an unbiased estimate cannot be determined. d. .47

d. .47

The number of vehicle thefts in the parking lot of a shopping mall varies from month to month. Assume that the number of thefts(x) at the shopping mall has the following probability distribution. x | f(x) 0 .60 1 .25 2 .15 3 .05 The mean number of thefts per month is: a. 6 b. .175 c. 1.5 d. .70

d. .70

A university is interested in the average age of its students. A simple random sample of 30 students was selected. The following descriptive statistics for their ages were compted: x̄ =20.8 and s^2=8.4. What is a point estimate of the population standard deviation for age? a. 8.4 b. 20.8 c. 70.6 d. 2.9

d. 2.9

Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is: a. 75 b. .03 c. 30 d. 235

d. 235

A pediatrician records the heights and ages of her patients over a one month period. The average height is recorded for each age and is an example of a: a. continuous random variable. b. discrete random variable. c. None of these choices are correct. d. complex random variable.

a. continuous random variable.

Which of the following is not a required condition for a discrete probability function? a. ∑f(x) = 1 b. ∑f(x) ≥ 0 for all values of x c. ∑f(x) = 0 d. All of these choices are correct.

c. ∑f(x) = 0

The number of simple random samples of size 20 that can be selected from a finite population of size 25 is: a. 53,130 b. 1 c. 20 d. 120

a. 53,130

A production manager has provided the following information about the probabilities of the number of faulty products produced per week. X | F(x) 0 .16 1 .35 2 .42 3 .09 4 .01 Is this a valid probability distribution? If not, why? Is this a valid probability distribution? If not, why? a. It is not a valid probability distribution because ∑f(x) > 1. b. It is not a valid probability distribution because ∑f(x) < 1. c. It is not a valid probability distribution because f(O) ≠ 0. d. Yes, it is a valid probability distribution.

a. It is not a valid probability distribution because ∑f(x) > 1.

A binomial experiment is conducted in which 30 dishwashers are randomly selected from a production plant and tested to determine whether or not they function properly. Any specific dishwasher will work properly with a probability of p =.98. What is the random variable in this experiment? a. The number of dishwashers that work properly from the 30 selected b. One dishwasher and whether it works properly c. The 30 dishwashers d. The probability that the dishwasher works properly

a. The number of dishwashers that work properly from the 30 selected

The sample mean, x̄, obtained from repeated samples of the same size from a population is a. a random variable. b. always equal to 0. c. exactly equal to the population mean. d. always smaller than the population mean.

a. a random variable.

A dealership is interested in the population proportion of new vehicle purchases that are gold in color. Which of the following represents the sample statistic of interest? a.(p̂) b. μ c. n d. s

a.(p̂)

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.9370? a. 1.96 b. - 1.53 c. 1.50 d. .8264

b. - 1.53

Twelve percent of the customers of a bank overdraw their accounts at least once a month. A sample of eight customers is selected. What is the probability that exactly two customers in the sample will overdraw their account this month? a. .939 b. .187 c. .28 d. 0

b. .187

Suppose 8 out of 26 cars that pass a radar station are exceeding the speed limit. If the population proportion of cars that exceed the speed limit is .42, what is the value of p̂? a. .69 b. .31 c. 8 d. .42

b. .31

What is the P(10≤x≤30) for a uniform random variable defined on the interval 0 to 40? a. .025 b. .5 c. .05 d. 0

b. .5

The lodge at a ski resort has 50 suites. In the winter months, the occupancy rate for the suites is approximately 90%. What is the probability that 45 or fewer rooms are occupied on a given day? a. .5948 b. .5000 c. .9909 d. .4052

b. .5000

Assume the number of customers who order a dessert with their meal on a given night at a local restaurant has the probability distribution given below. x | f(x) 3 .25 4 .55 5 .15 6 .05 The variance for the random variable x is: a. .77 b. .60 c. .36 d. 4

b. .60

The proportion of students at a university who pass a biology class is p =.86. If 50 students are randomly selected, what is the probability that at least 75% of them have passed the class? a. .9638 b. .9875 c. .0362 d. .0125

b. .9875

The lodge at a ski resort has 50 suites. In the winter months, the occupancy rate for the suites is approximately 90%. What is the probability that at least 80% of the suites are occupied on a given day? a. .1662 b. .9908 c. .5714 d. Not enough information is give to answer the question.

b. .9908

Which of the following represents the mean of the normal distribution used to approximate a binomial distribution? a. μ=√np(1-p) b. 0 c. μ=np d. μ=n(1-p)

c. μ=np

Starting salaries of a sample of five management majors along with their genders are shown below. Employee|Salary($1000s)|M/F 1 | 30 | F 2 | 28 | M 3 | 22 | F 4 | 26 | F 5 | 19 | M If we select simple random samples of size 2 from the given data, what is the probability of any of the five employees being selected first? a. 0.40 b. 0.20 c. 0.50 d. 0.10

b. 0.20

Of the passengers on a 757 airliner, 40% are female. A random sample of 25 passengers is selected. What is the expected number of female passengers in the sample? a. 40 b. 10 c. 6 d. 25

b. 10

Given the sampling distribution of the sample mean shown here, which of the following values is a reasonable estimate for the population mean? (highest bar is at 300) a. 280 b. 300 c. 0.27 d. 320

b. 300

When using the normal approximation to the binomial, what is the standard deviation for a binomial probability distribution with p =.3 and n = 145? a. 43.5 b. 5.52 c. 11.5 d. 30.45

b. 5.52

The CEO of a large corporation is interested in the average salary of all managers for his large corporation. A sample of 500 managers found the average salary to be $56,500. Which of the following statements is correct? a. The average salary for all the managers will also be $56,500. b. The average salary for the 500 managers can be used to estimate the average salary for all managers. c. The population size is 500 managers. d. The value $56,500 is a parameter.

b. The average salary for the 500 managers can be used to estimate the average salary for all managers.

Suppose a binomial random variable consists of 9 trials with a success of probability of .4. What are the mean and standard deviation for this binomial random variable? a. The mean is 2 and the standard deviation is 2.16. b. The mean is 3.6 and the standard deviation is 1.47. c. The mean and standard deviation cannot be calculated from the information given. d. The mean is .4 and the standard deviation is 1.

b. The mean is 3.6 and the standard deviation is 1.47.

The amount of time a patient must wait to be seen at a doctor's office is an example of: a. either a continuous or a discrete random variable, depending on the gender of the individual. b. a continuous random variable. c. a discrete random variable. d. either a continuous or a discrete random variable, depending on the type of doctor's office.

b. a continuous random variable.

Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,000. If a random sample of size 25 is taken and the mean is calculated, what is the probability that the mean value will be between $62,500 and $64,000? a. 0.1465 b. 0.0371 c. 0.2005 d. 0.0827

c. 0.2005

A sample of 240 is selected from a finite population of 500. If the standard deviation of the population is 44, what is the standard error of the sample mean? a. 4.20 b. 1.42 c. 2.05 d. 2.84

c. 2.05

A simple random sample of 8 high school student's ACT scores gave the following data. 27, 30, 20, 29, 28, 36, 34, 31 What is a point estimate for μ, the mean test score for the population? a. 235 b. 4.84 c. 29.38 d. A point estimate cannot be computed since the data for the whole population are not available.

c. 29.38

Suppose a random variable t has a probability distribution defined by f(t) = t/20 for t = 2, 4, 6, and 8. What is the expected value for t? a. 1.5 b. 2 c. 6 d. 5

c. 6

The random variable x is the number of vehicles that pass through an intersection in a 30 minute interval. 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 30 minutes is 9. What is the expected value of the random variable x? a. 3 b. 2.7 c. 9 d. 30

c. 9

Which of the following distributions is not symmetric? a. Normal b. All of these choices distributions are symmetric c. Exponential d. Standard normal

c. Exponential

When can the central limit theorem be used to approximate the sampling distribution of x̄ by a normal curve? a. It can be used when the standard deviation of the population is normally distributed. b. It can be used only when the population distribution is normal. c. It can be used when the population distribution is not normal and n is greater than 30. d. It can be used when the population is skewed and n is less than 20.

c. It can be used when the population distribution is not normal and n is greater than 30.

Residents who own a house in a particular city were divided into 15 groups based on the location of their house. A random sample of ten residents from each of the 15 groups was selected to be interviewed. What type of sampling plan is being used? a. Cluster sampling b. Judgment sampling c. Stratified random sampling d. Systematic sampling

c. Stratified random sampling

Which of the following is a continuous random variable? a. The number of goals scored in a hockey game b. The number of correct answers on a multiple choice test c. The heights of children in a preschool d. The number of houses for sale in a city

c. The heights of children in a preschool

Which of the following could represent a discrete uniform probability function? a. f(x) = 5 n where n is the number of values the random variable can assume b. f(x) = 4^x c. f(x) = 1/6 d. f(x) = 6/5

c. f(x) = 1/6

A sample chosen by stratified random sampling involves: a. randomly selecting one of the first k elements in an ordered population, and then selecting every kth element in the population thereafter. b. selecting a simple random sample of clusters from the available clusters in the population. c. selecting a simple random sample from each of a given number of strata formed from the elements in the population. d. a sample chosen by a knowledgeable person on the subject of the study.

c. selecting a simple random sample from each of a given number of strata formed from the elements in the population.

The normal distribution is symmetric about: a. the standard deviation. b. 0 c. the mean. d. 1

c. the mean.

If a random sample of size n = 20 is taken from a normal distribution with a mean μ, which of the following would be an unbiased estimator for μ? a.p̂ b. ? c. x̄ d. s

c. x̄

For which of the following sampling methods can the sampling distribution of the sample statistics generally be identified? a. cluster sampling b. simple random sampling c. systematic sampling d. All of these choices are correct.

d. All of these choices are correct.

A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into ten sections and randomly select four sections to survey the number of moose present. What sampling method is being used? a. Systematic sampling b. Judgment sampling c. Stratified random sampling d. Cluster sampling

d. Cluster sampling

A retailer received seven new items from the manufacturer. Four of the items were damaged in transit. The retailer sold three items to five customers. Which of the following probability distributions would be useful in this situation? a. Poisson probability distribution b. Binomial probability distributions c. Uniform probability distribution d. Hypergeometric probability distribution

d. Hypergeometric probability distribution

A manufacturer is interested in the number of flaws occurring in each 30 yards of material. The random variable representing the number of major flaws satisfies which of the following probability distributions? a. Binomial b. Not enough information is given to answer this question. c. Normal d. Poisson

d. Poisson

A continuous random variable may assume: a. only the positive integer values in an interval. b. only fractional values in an interval or collection of intervals. c. only integer values in an interval or collection of intervals. d. any value in an interval or collection of intervals.

d. any value in an interval or collection of intervals.

Suppose s random sample of 20 observations is taken from an infinite population. The sampling distribution of p̂ is a. not normal since n < 30 b. approximately uniform because p is always normally distributed c. approximately normal if np > 30 and n(1 - p) > 30 d. approximately normal if np ≤ 5 and n(1 - p)≤ 5

d. approximately normal if np ≤ 5 and n(1 - p)≤ 5

If the sample size is increased, the standard error of the sampling distribution of x̄ will a. It depends on the data being studied. b. remain the same. c. increase. d. decrease.

d. decrease.

If a random variable can assume one of five outcomes and the distribution is uniform, what is the probability function for this random variable? a. f(x) = 5 b. f(x) = x5 c. f(x) = 1/5x d. f(x) = .20

d. f(x) = .20