stats midterm

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?

$29.40

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor's degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor's degree. What is the probability that B will equal 40 ?

(4050​)(0.31)40(0.69)10

According to a recent survey, 81 percent of adults in a certain state have graduated from high school. If 15 adults from the state are selected at random, what is the probability that 5 of them have not graduated from high school?

(515​)(0.19)5(0.81)10

Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them to catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon?

0.2(0.8)7

The following question(s) refer to the following scenario and set of data. In the 1830s, land surveyors began to survey the land acquired in the Louisiana Purchase. Part of their task was to note the sizes of trees they encountered in their surveying. The table of data below is for bur oak trees measured during the survey. Which of the following differences in cumulative relative frequencies gives the proportion of trees that are 12 inches to 16 inches, inclusive, in diameter?

0.726-0.325

The following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. Number of Books01234567Probability0.350.200.150.100.070.080.040.01 Let the random variable B represent the number of books a student buys at the next book fair. What is the expected value of B?

1.79

A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is 1 or 2. How many dice should the player choose to roll to maximize the chance of winning?

2

A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?

2

According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. If a sample of 250 Colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in Colorado?

7.82

In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?

A gain of about 83 points

A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured?

Approximately normal

In which of the following should the random variable X not be modeled with a geometric distribution?

In a bag of 30 different colored candies, about 20% are red. One candy will be selected one at a time without replacement, and its color will be recorded. Let X represent the number of candies selected before red is selected.

Let S represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait. The random variable S follows a geometric distribution with mean 4.66. Which of the following is a correct interpretation of the mean?

In repeated sampling from the distribution of S, the average of the values will approach 4.66.

A fair die has its faces numbered from 1 to 6. Let random variable F represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5 and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded.

Mean 3.5 and standard deviation 0.7638

Let random variable U represent the field goal percentage (percentage of shots made) for players in a basketball league. The following table shows the probability distribution of the random variable U. Field Goal PercentageProbability0.30.100.40.450.50.300.60.100.70.05 Fatima claims that the distribution of U is uniform with a median of 0.4 field goal percentage. Is Fatima's claim supported by the table?

No, the distribution is skewed to the right with a median of 0.4 field goal percentage.

Which of the following graphs represents a binomial distribution with n = 20 and p = 0.25?

highest at five

For a certain population of sea turtles, 18 percent are longer than 6.5 feet. A random sample of 90 sea turtles will be selected. What is the standard deviation of the sampling distribution of the sample proportion of sea turtles longer than 6.5 feet for samples of size 90 ?

\sqrt{\frac{0.18\left(1-0.18\right)}{90}}900.18(1−0.18)​​

Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p̂?

n = 100 and p close to 1/2

The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. A random sample of 16 students will be selected and the mean number of pets for the sample will be calculated. What is the mean of the sampling distribution of the sample mean for samples of size 16 ?

3.2

A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?

$432.00

The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosen at random, one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independent. Which of the following is closest to the probability that X > 3; that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?

0.493

According to a survey about how workers get to work in Wyoming, 77 percent of workers get to work by driving alone, 11 percent get to work by carpooling, 4 percent get to work by walking, and 8 percent get to work by other means of transportation. Suppose a sample of 200 Wyoming workers is selected at random. Let the random variable D represent the number of workers in the sample who get to work by driving alone. What is the expected value of D?

154

A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y ?

17.5

A machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution?

234 grams

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

A sample of size 25 will produce more variability of the estimator than a sample of size 50.

A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. All 10 dice were rolled, and the average of the 10 numbers appearing faceup was recorded. The process was repeated 20 times. Which of the following best describes the distribution being simulated?

A sampling distribution of a sample mean with n = 10, μx̄ = 3.5, and σx̄ ≈ 0.54

The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations. Which of the following is the correct ordering of the graphs from least value of n to greatest value of n ?

A, C, B

A company that ships crystal bowls claims that bowls arrive undamaged in 95 percent of the shipments. Let the random variable G represent the number of shipments with undamaged bowls in 25 randomly selected shipments. Random variable G follows a binomial distribution with a mean of 23.75 shipments and a standard deviation of approximately 1.09 shipments. Which of the following is the best interpretation of the mean?

For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

On any given day, the proportion of workers at a factory who are more than 5 minutes late to work is 0.11. A random sample of 20 workers will be selected. Which of the following is the best interpretation of the mean of the sampling distribution of the sample proportion of workers in the sample who are more than 5 minutes late to work for samples of size 20 ?

For all samples of size 20, the mean of all possible sample proportions is equal to 0.11.

A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let p_dpd​ represent the population proportion of all cell phone screens with a screen defect, therefore p_d=0.05pd​=0.05. For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample size 400, \mu_{p_d}=0.05μpd​​=0.05. Which of the following is the best interpretation of \mu_{p_d}=0.05μpd​​=0.05?

For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

At a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. A random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P\left(\overline{x}>22\right)\approx0.05P(x>22)≈0.05?

For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

For which of the following is the shape of the sampling distribution of the sample mean approximately normal? A random sample of size 5 from a population that is approximately normal A random sample of size 10 from a population that is strongly skewed to the right A random sample of size 60 from a population that is strongly skewed to the left

I and III only

Let the random variable Q represent the number of students who go to a certain teacher's office hour each day. The standard deviation of Q is 2.2. Which of the following is the best interpretation of the standard deviation?

On average, the number of students going to an office hour varies from the mean by about 2.2 students.

The distribution of age for players of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2 years. Consider a random sample of 4 players and a different random sample of 50 players from the population. Which of the following statements is true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50 ?

Only the sampling distribution for size 50 will be approximately normal, and the mean for both will be 26.8.

The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ?

P(N = 8)

The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0.156?

P(N = 8)

According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)

P(z>300(0.22)(0.78)​​0.27−0.22​)

At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?

Sampling without replacement will result in a standard deviation less than but close to \sqrt{\frac{0.4\left(0.6\right)}{500}}.5000.4(0.6)​​.

Data will be collected on the following variables. Which variable is most likely to be approximated by a normal model?

The distribution of life span, in minutes, for batteries of a certain size, where most life spans cluster around the center of the distribution but with some very low and some very high life spans

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer's batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.

Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Which of the following is the best description of a dotplot created from the 100 sample means?

The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon.

Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean?

The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014, let the random variable C represent the number of households in the sample that had a computer. What are the mean and standard deviation of C?

The mean is 170 households, and the standard deviation is 5.05 households.

If a probability distribution is symmetric, which of the following statements must be true?

The mean of the distribution is equal to the median of the distribution.

A certain factory that manufactures office chairs has a quality control process to identify defective chairs. The binomial random variable D represents the number of chairs in a sample of chairs that are defective. The mean of D is 10 chairs and the standard deviation is 3 chairs. Based on the distribution of D, which of the following would be an accurate interpretation of the value 0.1 ?

The probability of identifying a defective chair

A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation. Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

The sample size was not sufficiently large.

At a large corporation, the distribution of years of employment for the employees has mean 20.6 years and standard deviation 5.3 years. A random sample of 100 employees was selected and surveyed about employee satisfaction. The sample of employees had a mean 20.3 years and standard deviation 6.1 years. Remy claims that the mean of the sampling distribution of the sample mean for samples of size 100 is 20.6 years. Is Remy's claim correct?

Yes. The mean of the sampling distribution is 20.6 years.

A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable X represent the weight of fleece produced by a sheep from Northern Farm. The distribution of X has mean 14.1 pounds and standard deviation 1.3 pounds. Let the random variable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution of Y has mean 6.7 pounds and standard deviation 0.5 pound. Assume X and Y are independent. Let W equal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomly selected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W ?

\sqrt{10\left(1.3\right)^2+15\left(0.5\right)^2}10(1.3)2+15(0.5)2​

A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of 50 trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described?

highest at nine, really tall

The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?

n=10 only

The histogram below represents data obtained after the census of an entire population was conducted. The sampling distribution of the sample mean based on samples of size 2 for the population was simulated, and a histogram of the results was produced. Which of the following histograms is most likely the histogram of that sampling distribution?

one big in middle and small bumps on edges

Let random variable X represent the the number of visitors to a certain museum during a given day. The following table shows the probability distribution of the random variable. Which of the following claims about the distribution of random variable X is best supported by the histogram?

On a given day, it is equally likely for the museum to have less than 300 visitors as it is to have more than 300 visitors.

Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?

0

The distribution of time needed to complete a certain programming task is approximately normal, with mean 47 minutes and standard deviation 6 minutes. Which of the following is closest to the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete?

0.0303

Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute times is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. Which of the following is closest to the probability that Carly's commute time tomorrow will be greater than 25 minutes?

0.0950

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

0.2743

Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varies due to weather conditions and other factors. The daily water level has a distribution that is approximately normal with mean water level of 84.07 feet. The probability that the daily water level in the lake is at least 100 feet is 0.064. Which of the following is closest to the probability that on a randomly selected day the water level in the lake will be at least 90 feet?

0.29

A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone?

0.29,1000(0.29)(0.71)​

Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt 5 shots of the arrow and that each shot is independent from the others. Let the random variable X represent the number of times he hits the inner ring of the target in 5 attempts. The probability distribution of X is given in the table. What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X ?

0.40951

An experiment was conducted in which planks of wood painted red and green were shown to pigeons to investigate a pigeon's ability to select a certain color. Pigeons could accurately select the color of the plank of wood 20 percent of the time. A simulation was conducted in which a trial consisted of a pigeon being shown eight planks of wood and its number of successes being recorded. This process was repeated many times, and the results are shown in the histogram. Based on the results of the simulation, which of the following is closest to the probability that there were at most three successes in a trial?

0.94

Clara recorded 50 numerical observations on a certain variable and then calculated the mean \overline{x}x and the standard deviation s for the observations. To help decide whether a normal model is appropriate, she created the following chart. In Clara's chart, the letters a, b, c, d, and e represent the number of observations falling in each interval. Which of the following list of counts for a, b, c, d, and e respectively, is the best indicator that the variable can be modeled with a normal approximation?

1, 7, 34, 7, 1

For a certain dog breed, the number of puppies in a litter typically varies from 2 to 6. The following table shows the probability distribution of the random variable N, where N represents the number of puppies in a litter. Also shown are the squared deviations, or distances, from the expected value of 4.5 for the distribution. Number of puppies23456Squared deviation6.252.250.250.252.25Probability0.050.150.250.350.20 What is the variance of the distribution?

1.25

At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6(doughnuts)^2, respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P ?

1.5\sqrt{3.6}1.53.6​

A company ships gift baskets that contain apples and pears. The distributions of weight for the apples, the pears, and the baskets are each approximately normal. The mean and standard deviation for each distribution is shown in the table below. The weights of the items are assumed to be independent. Let the random variable W represent the total weight of 4 apples, 6 pears, and 1 basket. Which of the following is closest to the standard deviation of W ?

1.97 ounces

Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange. Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?

13.75 and 2.905

According to a recent survey, 47 percent of the people living in a certain region carry a certain genetic trait. People from the region will be selected at random one at a time until someone is found who carries the genetic trait. Let the random variable G represent the number of people selected to find one person who carries the genetic trait. On average, how many people from the region will need to be selected to find one person who carries the genetic trait?

2.13

A fair coin is flipped 10 times and the number of heads is counted. This procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?

22, 24, 18

A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?

29.0

The random variable W has a geometric distribution with p = 0.25. Approximately how far do the values of W typically vary, on average, from the mean of the distribution?

3.46

The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation \sigma_xσx​ Which of the following is the best estimate of the standard deviation of the population, \sigma_xσx​?

75

A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company's claim is correct, what is the expected number of nondefective lightbulbs in a random sample of 1,000 bulbs?

980

For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?

A random sample of 10 taken from a population distribution that is skewed to the right

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

Approximately normal with mean $206,274 and standard deviation $3,788

A sample of size n will be selected from a population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?

Both np and n(1 - p) are at least 10

The distribution of prices for a certain car model is approximately normal with mean $21,800 and standard deviation $400. A random sample of 4 cars of the model will be selected. What is the correct unit of measure for the mean of the sampling distribution of \overline{x}?x?

Dollars

A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively. Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters?

Mean 4.9 letters and standard deviation 1.5 letters

Let random variable Y represent the number of interviews conducted for job openings at a certain company. The following table shows the cumulative probability distribution of the discrete random variable Y. yP(Y<=y)5060.270.480.690.8101.0 Khaleed claims that the distribution of Y is skewed to the left with mean equal to 8 interviews. Is Khaleed's claim correct?

No, the distribution is uniform with mean equal to 8 interviews.

The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

On average, the number of breakdowns per day varies from the mean by about 0.28.

Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300 ?

The bias will remain the same and the variance will decrease.

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

City officials estimate that 46 percent of all city residents are in favor of building a new city park. A random sample of 150 city residents will be selected. Suppose that 51 percent of the sample are in favor of building a new city park. Which of the following is true about the sampling distribution of the sample proportion for samples of size 150 ?

The distribution is approximately normal, and the mean is 0.46.

The mean and standard deviation of the sample data collected on continuous variable x are -0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals. IntervalRelative Frequency-0.34\le x\le-0.31−0.34≤x≤−0.310.02-0.31\le x\le-0.28−0.31≤x≤−0.280.15-0.28\le x\le-0.25−0.28≤x≤−0.250.33-0.25\le x\le-0.22−0.25≤x≤−0.220.36-0.22\le x\le-0.19−0.22≤x≤−0.190.11-0.19\le x\le-0.16−0.19≤x≤−0.160.03 Based on the table, do the data support the use of a normal model to approximate population characteristics?

Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.