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Q:
If the sample size n is infinitely large, then s2 is an unbiased estimator of 2.
Q:
The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.
Q:
The mean of the sampling distribution of is always equal to the mean of the sampled population.
Q:
The standard deviation of the sampling distribution of the sample mean is .
Q:
As the sample size increases, the standard deviation of the sampling distribution increases.
Q:
If the sampled population distribution is skewed, then in most cases the sampling distribution of the mean can be approximated by the normal distribution if the sample size n is at least 30.
Q:
If p = .9 and n = 40, then we can conclude that the sampling distribution of is approximately a normal distribution.
Q:
If p = .8 and n = 50, then we can conclude that the sampling distribution of is approximately a normal distribution.
Q:
If a population is known to be normally distributed, then it follows that the sample mean must equal the population mean.
Q:
If the sampled population is exactly normally distributed, then the sampling distribution of is also expected to be normal, regardless of the sample size.
Q:
If a population is known to be normally distributed, then it follows that the sample standard deviation must equal .
Q:
The Central Limit Theorem states that as sample size increases, the population distribution more closely approximates a normal distribution.
Q:
The standard deviation of all possible sample proportions increases as the sample size increases.
Q:
The reason sample variance has a divisor of n - 1 rather than n is that it makes the variance an unbiased estimate of the population variance.
Q:
A minimum-variance unbiased point estimate has a variance that is as small as or smaller than the variances of any other unbiased point estimate.
Q:
A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.
Q:
The sampling distribution of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.
Q:
For any sampled population, the population of all sample means is approximately normally distributed.
Q:
The sampling distribution of must be a normal distribution with mean = 0 and standard deviation = 1.
Q:
A sample size of 500 is sufficiently large to conclude that the sampling distribution of is a normal distribution, when the estimate of the population proportion is .995.
Q:
If we have a sample size of 100 and the estimate of the population proportion is .10, we can estimate the sampling distribution of with a normal distribution.
Q:
The weight of a product is normally distributed with a mean of four ounces and a variance of .25 squared ounces. What is the probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces?
A. .0228
B. .9772
C. 0.000
D. 1.00
Q:
If x is a binomial random variable where n = 100 and p = .1, find the probability that x is less than or equal to 10, using the normal approximation to the binomial.A. .5675B. .0170C. .5714D. .4325
Q:
The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 29.75 and 30.5 inches long?
A. .4332
B. .4878
C. .0546
D. .9210
Q:
The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random will be less than 31 inches long?
A. 0.00
B. 1.00
C. .8289
D. .5987
Q:
The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 30.25 and 30.65 inches long?
A. .9987
B. .1574
C. .1587
D. .8413
Q:
The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random will be less than 29.75 inches long?
A. .8944
B. .1056
C. .9332
D. .0668
Q:
Consider a normal population with a mean of 10 and a variance of 4. Find P(X 10).A. 1.00B. 0.00C. 0.50D. -0.50
Q:
Consider a normal population with a mean of 10 and a variance of 4. Find P(X > 18).
A. 1.00
B. 0.00
C. .9772
D. .0228
Q:
Consider a normal population with a mean of 10 and a variance of 4. Find P(X > 7).
A. .0668
B. .9332
C. .8413
D. .1587
Q:
Consider a normal population with a mean of 10 and a variance of 4. Find P(X < 6).
A. .0228
B. .1587
C. .8413
D. .9772
Q:
If the mileage per gallon for a car is normally distributed, 32 mpg has a z score of 1.2, and 24 mpg has a z score of -.4, what is the mean mpg of the distribution?A. 28B. 26C. 30D. 38
Q:
Suppose the daily change in price of a stock is normally distributed with mean = .20 and standard deviation = .30. What price change is associated with the 25th percentile?A. .1925B. .2075C. .401D. -.001
Q:
An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. What raw score corresponds to the 70th percentile?
A. 77.4
B. 83.5
C. 82.6
D. 76.5
Q:
An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. What proportion of tests has scores over 90?A. .9772B. .0228C. .9544D. .0456
Q:
The time between breakdowns of an alarm system is exponentially distributed with mean 10 days. What is the probability that there are no breakdowns on a given day?A. .9048B. .3679C. .0952D. 0.000
Q:
The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime is greater than or equal to 700 days?
A. .7603
B. .5034
C. .2397
D. .4966
Q:
The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime exceeds 1,000 days?
A. .6321
B. .5000
C. .3679
D. 1.000
Q:
The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?
A. .6321
B. .5507
C. .7135
D. .4493
Q:
The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last more than 1,200 hours?A. .3012B. .3679C. .4345D. .6988
Q:
What is the probability that a standard normal random variable will be between 0.3 and 3.2?A. .6179B. .3814C. .3808D. .9993
Q:
What is the probability that a standard normal random variable will be between -2 and 2?A. .4772B. .0228C. .9772D. .9544
Q:
The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly between 4.70 and 4.82 hours?
A. .1336
B. .8664
C. .9332
D. .4332
Q:
The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly more than 4.80 hours?
A. .1587
B. .8413
C. .6587
D. .3413
Q:
The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly less than 4.66 hours?A. -.0062B. .5062C. .0062D. .9938
Q:
The probability that an appliance is currently being repaired is .5. If an apartment complex has 100 such appliances, what is the probability that at least 60 are currently being repaired? Use the normal approximation to the binomial.
A. .5000
B. .0287
C. .6000
D. .9713
Q:
If x is a binomial random variable where n = 100 and p = .1, find the probability that x is less than or equal to 10, using the normal approximation to the binomial.
A. .9544
B. .0446
C. .5675
D. .4325
Q:
Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it between 50 feet and 60 feet?
A. .9972
B. .5000
C. .9544
D. .4772
Q:
Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it no less than 55 feet?
A. .8413
B. .1587
C. .6826
D. .3174
Q:
The time it takes a woman to travel from her apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes. If she leaves home at 9:05 a.m., what is the probability that she will get to the station between 9:25 and 9:30 a.m.?
A. 1.0
B. 0
C. 0.5
D. 0.25
Q:
If the random variable of x is normally distributed, _____ percent of all possible observed values of x will be within two standard deviations of the mean.
A. 99.73
B. 68.26
C. 95.00
D. 95.44
Q:
The standard deviation of a standard normal distribution is always equal to ____________.A. 1B. 0.5C. 0D. -1
Q:
The mean of a standard normal distribution is always equal to ____________.A. 1B. 0.5C. 0D. -1
Q:
_____________ values of the standard deviation result in a normal curve that is narrower and
more peaked.
A. Smaller
B. Equal
C. Larger
D. Uniform
Q:
____________ values of the standard deviation result in a normal curve that is wider and flatter.
A. Smaller
B. Equal
C. Larger
D. Uniform
Q:
The thickness of a randomly selected metal piece is a ___________ random variable.
A. Poisson
B. continuous
C. discrete
D. binomial
Q:
A normal distribution with mean equal to zero and a standard deviation equal to one is called the ____________ normal distribution.
A. continuous
B. uniform
C. exponential
D. standard
Q:
Given that X is a normal random variable, the probability that a given value of X is below its mean is ________________.
A. 1
B. equal to 0.5
C. less than 0.5
D. greater than 0.5
Q:
The area under the curve of a valid continuous probability distribution must ____________.
A. equal 1
B. be between 0 and 1
C. be infinite
D. be less than 1
Q:
The number of standard deviations that a value x is from the mean is a(n) ____________.
A. variance
B. exponential value
C. z score
D. area
Q:
The specific shape of each normal distribution is determined by its ____________ and ____________.
A. mean, standard deviation
B. median, standard deviation
C. mean, variance
D. median, variance
Q:
A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers is a(n) ____________ distribution.
A. exponential
B. binomial
C. normal
D. uniform
Q:
A probability distribution that describes the time or space between successive occurrences of an event is a(n) ____________ probability distribution.
A. binomial
B. uniform
C. exponential
D. normal
Q:
____________ theory is a methodology that attempts to determine the number of servers that strikes an optimum balance between the time customers wait for service and the cost of providing service.
A. Exponential
B. Binomial
C. Uniform distribution
D. Queuing
Q:
The z value tells us the number of ____________ that a value of x is from the mean.
A. variances
B. standard deviations
C. medians
D. standard means
Q:
A continuous probability distribution that is useful in describing the time or space between successive occurrences of an event is a(n)
A. uniform probability distribution.
B. normal probability distribution.
C. Poisson probability distribution.
D. exponential probability distribution.
Q:
When a ____________ probability distribution is used to approximate a ____________ probability distribution, we must make a ____________ correction.
A. continuous, discrete, continuity
B. discrete, continuous, continuity
C. continuous, discrete, finite population
D. None of the other choices is correct.
Q:
If the random variable x is normally distributed, ______ percent of all possible observed values of x will be within three standard deviations of the mean.
A. 68.26
B. 95.44
C. 99.73
D. 100
E. None of the other choices is correct.
Q:
Which of the following statements is not a property of the normal probability distribution?
A. The normal distribution is symmetric.
B. 95.44 percent of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean.
C. The mean, median, and mode are equal.
D. The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean.
E. All of the other answers are properties of the normal distribution.
Q:
The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. We calculated the value of z for a specific box of this brand of cereal, and the z value was negative. This negative z value indicates that
A. we made a mistake in our calculations, as z must always be a nonnegative number.
B. the fill weight exceeds 910 grams.
C. the fill weight is less than 910 grams.
D. the fill weight is equal to 910 grams.
E. the fill weight may be more or less than 910 grams depending on the value of the standard deviation.
Q:
The relationship between the standard normal random variable z and normal random variable X is thatA. only the normal random variable X is continuous.B. only the standard normal variable z is continuous.C. the standard normal variable z counts the number of standard deviations that the value of the normal random variable X is away from its mean.D. the values of the standard normal random variable z cannot be negative.E. the values of the normal random variable X cannot be negative.
Q:
A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is
A. 40 percent.
B. 20 percent.
C. 10 percent.
D. 30 percent.
E. 16.7 percent.
Q:
The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that he scored
A. higher than 16 percent of the class.
B. higher than 45 percent of the class.
C. above the first quartile.
D. below the mean.
E. lower than 16 percent of the class.
Q:
If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour
A. is greater than the proportion earning less than $13 per hour.
B. is greater than the proportion earning less than $18 per hour.
C. is less than 50 percent.
D. is less than the proportion earning more than the mean wage.
Q:
The normal approximation of the binomial distribution is appropriate whenA. np 5.B. n(1 - p) 5.C. np 5.D. n(1 - p) 5 and np 5.E. np 5 and n(1 - p) 5.
Q:
The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution. In this industry, a firm with a standard normal variable value of z = 1
A. has an above average price-to-earnings ratio.
B. has a below average price-to-earnings ratio.
C. has an average price-to-earnings ratio.
D. may have an above average or below average price-to-earnings ratio.
Q:
Which of the following is a continuous distribution?
A. Poisson
B. hypergeometric
C. exponential
D. binomial
Q:
If the random variable X has a mean of and a standard deviation , then the mean and standard deviation, respectively, of (X - )/ areA. and .B. and s.C. 1 and 0.D. 0 and 1.
Q:
Values of the standard normal random variable are measured
A. with reference to specific units.
B. in the units in which the mean is measured.
C. in the number of standard deviations from the mean.
D. in squared units in which the mean is measured.
E. None of the choices is correct.
Q:
The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.
A. less than
B. greater than
C. equal to
D. less than, greater than, or equal to, depending on the value of the mean,
E. less than, greater than, or equal to, depending on the value of the standard deviation,