Q&A Hero

Q: If we have a sample size of 100 and the estimate of the population proportion is .10, what is the mean of the sampling distribution of the sample proportion? A. 0.0009 B. 0.10 C. 0.03 D. 0.90 E. 0.09

Q: A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lb and 24 lb, respectively, then based on a sample size of 36 boxes, what is the probability that the average weight of the boxes will be less than 84 lb? A. 16.87% B. 93.32% C. 43.32% D. 6.68% E. 84.13%

Q: A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lb and 24 lb, respectively, then based on a sample size of 36 boxes, what is the probability that the average weight of the boxes will exceed 94 lb? A. 34.13% B. 84.13% C. 15.87% D. 56.36% E. 16.87%

Q: The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. What percentage of sample means will be less than 5.14 inches? A. 0.043% B. 22.66% C. 4.3% D. .00043%

Q: The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Find the interval that contains 95.44 percent of the sample means. A. [5.04, 5.36] B. [5.18, 5.22] C. [5.16, 5.24] D. [5.07, 5.33]

Q: The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Calculate the standard deviation of the sampling distribution of the sample mean. A. 5.2 B. 0.018 C. 0.08 D. 0.063

Q: The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Calculate the mean of the sampling distribution of the sample mean. A. 5.2 B. 0.8 C. 0.08 D. 0.018

Q: A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are = 3.5 and = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is the probability that the random sample of 100 male students has a mean GPA greater than 3.42?A. .0548B. .4364C. .9452D. .5636

Q: A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are = 3.5 and = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Find the interval that contains 95.44 percent of the sample means for male students.A. [3.45, 3.55]B. [2.50, 4.50]C. [3.35, 3.65]D. [3.40, 3.60]

Q: A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are = 3.5 and = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Calculate .A. 0.5B. 3.5C. 7.0D. 0.05

Q: A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are = 3.5 and = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is ?A. 0.5B. 3.5C. 7.0D. 0.05

Q: It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected, what is the probability that the sample mean will be less than 0.84 seconds? A. .1151 B. .4522 C. .8849 D. .5478

Q: It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected, 80 percent of the sample means will be between what two values symmetrically distributed around the population mean? A. [.648, 1.152] B. [.836, .964] C. [.514, 1.280] D. [.858, .942]

Q: It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected, calculate the standard deviation of the sampling distribution of the sample mean. A. 0.3 B. 0.15 C. 0.9 D. 0.05

Q: It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected, calculate the mean of the sampling distribution of the sampling mean. A. 0.3 B. 0.15 C. 0.9 D. 0.05

Q: It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 23 download times are selected, describe the shape of the sampling distribution and how it was determined. A. normal; size of sample meets the Central Limit Theorem requirement B. normal; the original population is normal C. skewed; the original population is not a normal distribution D. cannot be determined with the information that is given

Q: In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. For the sake of argument, assume that 51 percent of the actual voters in the state support the incumbent governor (p = 0.51). Calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor. A. .0166 B. .0247 C. .0082 D. .9918

Q: In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. What is? A. .00825 B. .0166 C. .0247 D. .0003

Q: In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. From the 900 respondents, how many indicated that they would not vote for the current governor or indicated that they were undecided? A. 495 B. 450 C. 405 D. 400

Q: The chief chemist for a major oil and gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average of less than 3.85 ounces of this ingredient from 64 randomly inspected 1-gallon samples of regular unleaded gasoline? A. .1587 B. .8413 C. .1357 D. .8643

Q: The chief chemist for a major oil and gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average in excess of 4.3 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline? A. .5987 B. .4013 C. .9938 D. .0062

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 0.3 inches. What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long? A. .4602 B. .8413 C. .1587 D. .5397

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. A sample of four metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long? A. .9773 B. .0227 C. .0386 D. .0215

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 randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long? A. .0668 B. .9332 C. .0014 D. .4404

Q: Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.3 ounces. The weights of the sugar packages are normally distributed. What is the probability that 9 randomly selected packages will have an average weight in excess of 16.025 ounces? A. .5987 B. .0062 C. .4013 D. .9938

Q: A random sample of size 1,000 is taken from a population where p = .20. Find P( < .22). A. .2643 B. .9429 C. .9207 D. .0571

Q: A random sample of size 1,000 is taken from a population where p = .20. Find P( > .21). A. .2148 B. .0239 C. .9761 D. .7852

Q: A random sample of size 1,000 is taken from a population where p = .20. Find P( > .175). A. .9761 B. .0239 C. .0392 D. .9999

Q: A random sample of size 1,000 is taken from a population where p = .20. Find P( < .18). A. .9429 B. .0571 C. .2643 D. .0793

Q: A random sample of size 1,000 is taken from a population where p = .20. What is ? A. .0051 B. .03162 C. .01414 D. .01265

Q: A random sample of size 1,000 is taken from a population where p = .20. What is? A. .006 B. .20 C. .02 D. .16

Q: A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( < 51.5). A. .9641 B. .0359 C. .1389 D. .9999

Q: A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( > 50.5). A. .0002 B. .7257 C. .2743 D. .1389

Q: A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( < 48). A. .0082 B. .8330 C. .0999 D. .1389

Q: A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( > 49). A. .8331 B. .1151 C. .8849 D. .1389

Q: A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is? A. .1389 B. 5 C. 8.33 D. 0.833

Q: A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is x?A. 50B. 5C. 8.33D. 0.833

Q: Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points. A. .9015 B. .8030 C. .0155 D. .7939

Q: Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion. A. .0155 B. .9952 C. .9484 D. .9902

Q: The number of defectives in 10 different samples of 100 observations each is the following: 1, 2, 1, 0, 2, 3, 1, 4, 2, 1. What is the estimate of the population proportion of defectives? A. .017 B. .17 C. .016 D. .16

Q: The number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. What is the estimate of the population proportion of defectives? A. .25 B. .50 C. .05 D. .42

Q: Find P(395.4 < < 404.6), if the population mean = 400, x = 20, and n = 100.A. .9786B. .9999C. .0214D. .9893

Q: Find P( < 402), if = 400, x = 200, and n = 100.A. .8413B. .4602C. .5398D. .1587

Q: Find x, if = 400, P( < 396) = .0228, and n = 100.A. 0.20B. 200C. 20D. 2.00

Q: Find P( > 2,510) if = 2,500 and = 7.A. .0764B. .9998C. .9236D. .0001

Q: Find P( < 25) if = 16 and = 4.A. 1.000B. 2.25C. .9878D. .0122

Q: Find P( > 172), if = 175 and = 9.A. .1587B. .8413C. .6293D. .3707

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 0.3 inches. What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long? A. .8413 B. .6293 C. .3707 D. .1587

Q: Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.2 ounces. The weights of the sugar packages are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces? A. .0500 B. .3520 C. .9332 D. .0668

Q: A golf tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been placed in the front right corner of the green, and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.6 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 64 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes exceeding 4.75. A. .9938 B. .4013 C. .0062 D. .3783

Q: Find P( < 35) if = 40, x = 16, n = 16.A. .9944B. .4483C. .5517D. .1056

Q: A random sample of size 1,000 is taken from a population where p = .20. Describe the sampling distribution of . A. cannot be determined B. approximately normal C. skewed to the left D. skewed to the right

Q: A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5. The sampling distribution of ____________________. A. cannot be determined B. is skewed to the left C. is approximately normal D. is skewed to the right

Q: An unbiased estimate of 2 is _____.A. sB. s2C. D.

Q: The ___________ is a minimum-variance unbiased point estimate of the mean of a normally distributed population. A. sample mean B. sample variance C. sample standard deviation D. observed mean

Q: The ______________ of a sample statistic is the probability distribution of the population of all possible values of the sample statistic. A. sample mean B. sampling Distribution of Sample Mean C. probability D. observations

Q: The population of all _________________ proportions is described by the sampling distribution of . A. population B. random C. observed D. sample

Q: As the sample size ___________, the standard deviation of the population of all sample proportions increases. A. increases B. stays the same C. is variable D. decreases

Q: As the sample size increases, the variability of the sampling distribution of the mean ______________. A. increases B. stays the same C. is variable D. decreases

Q: A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as _______________. A. cluster sampling B. sampling error C. sampling distribution of the mean D. the Central Limit Theorem

Q: The sampling distribution of the sample mean is a normal distribution for ________ sample sizes, regardless of the shape of the corresponding population distribution. A. random B. large C. larger than 50 D. small

Q: The notation for the standard deviation of the sampling distribution of the sample mean is __________.A. B. xC. /nD.

Q: If the sampled population is finite and at least _____ times larger than the sample size, we treat the population as infinite. A. 5 B. 20 C. 30 D. 10

Q: The mean of the sampling distribution of the sample proportion is equal to _____ when the sample size is sufficiently large.A. B. pC. p x nD. (1 - p)

Q: According to the Central Limit Theorem, if a sample size is at least _____, then for most sampled populations, we can conclude that the sample means are approximately normal. A. 25 B. 20 C. 30 D. 50

Q: ____________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed. A. Cluster sampling B. Sampling error C. Sampling distribution of the mean D. The Central Limit Theorem

Q: For large samples, the sampling distribution of is approximately normal with a mean of _____.A. B. /nC. D. z

Q: The spread of the sampling distribution of is ____________ the spread of the corresponding population distribution sampling distribution. A. larger than B. smaller than C. the same as D. exactly

Q: For nonnormal populations, as the sample size (n) ___________________, the distribution of sample means approaches a(n) ________________ distribution. A. decreases, uniform B. increases, normal C. decreases, normal D. increases, uniform E. increases, exponential

Q: If a population distribution is known to be normal, then it follows that A. the sample mean must equal the population mean. B. the sample mean must equal the population mean for large samples. C. the sample standard deviation must equal the population standard deviation. D. the sample mean must equal the population mean, the sample mean must equal the population mean for large samples, and the sample standard deviation must equal the population standard deviation. E. None of the other choices is correct.

Q: Whenever the population has a normal distribution, the sampling distribution of is a normal or near normal distribution A. for only large sample sizes. B. for only small sample sizes. C. for any sample size. D. for only samples of size 30 or more.

Q: The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large isA. 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: If the sampled population has a mean of 48 and standard deviation of 16, then the mean and the standard deviation for the sampling distribution of for n = 16 are A. 4 and 1. B. 12 and 4. C. 48 and 4. D. 48 and 1. E. 48 and 16.

Q: Consider a sampling distribution formed based on n = 3. The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements .A. alwaysB. sometimesC. never

Q: As the sample size ______________, the variation of the sampling distribution of ___________. A. decreases, decreases B. increases, remains the same C. decreases, remains the same D. increases, decreases E. None of the other choices is correct.

Q: Consider two population distributions labeled A and B. Distribution A is highly skewed and nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality, A. population A will require a larger sample size. B. population B will require a larger sample size. C. populations A and B will require the same sample size. D. None of the other choices is correct.

Q: The Central Limit Theorem states that as the sample size increases, the distribution of the sample ____________ approaches the normal distribution. A. medians B. means C. standard deviations D. variances

Q: There is no easy way to calculate an unbiased point estimate of .

Q: The quantity [(N - n)(N - 1)] is called the finite population multiplier.

Q: The sample standard deviation s is an unbiased estimator of the population standard deviation .