The Empirical Rule tells the approximate percentage of the data which falls into certain ranges. To which distributions does the Empirical Rule​ apply?

Any normal distribution

A(n) ______can be used to compute probabilities of continuous random variables

probability density function

Both of the graphs represent normal distributions with a mean of muμequals=10. Determine which of the two normal distributions has a standard deviation of sigma equals 2σ=2 and which has a standard deviation of sigmaσequals=3. Explain how you know which is which.

Graph A has a standard deviation of sigmaσequals=2. Graph B has a standard deviation of sigmaσequals=3. Since Graph B is a wider​ graph, it has a greater spread and a larger standard deviation

There were 100 random samples of 100 individuals taken from a population which is known to have a moderately skewed distribution with some mean and a known standard deviation. A​ 95% confidence interval for the population mean was constructed for each of the 100 random samples using the​ one-sample z-methods. Which of the following statements is​ true?

Even though the population data are​ skewed, the distribution of sample means will be approximately normal because of the large sample size.​ Therefore, approximately​ 95% of the 100 confidence intervals constructed using the​ one-sample z-methods will capture the true population mean.

Eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting​ for, either North High School or South High School. From the results of his​ survey, Eric obtained a​ 95% confidence interval of​ (0.52,0.68) for the proportion of all adults in the city rooting for North High. What proportion of the 150 adults in the survey said they were rooting for North High​School?

0.60

Suppose a normal model has a mean of muμequals=​100, and​ 95% of the values are between 90 and 110. Which of the following must be true about the standard​ deviation?

The standard deviation must be approximately equal to 5.

The margin of error is​ _____________ the width of the confidence interval.

half

Days before a presidential​ election, an article based on a nationwide random sample of registered voters reported the following​ statistic, "52% ​(plus or minus±​3%) of registered voters will vote for Robert​ Smith." What is the ​"plus or minus±​3%" ​called?

margin of error.

The more variable the​ data, the​ _______ accurate the sample mean will be as an estimate of the population mean.

less

Identify which of the following statements is not a requirement for a probability density function or state that they all are.

The curve must be symmetric and centered at zero.

To find the​ z-score for a known​ area, use the​ _______ command on the calculator.

invNorm

A hungry college student just finished eating a large cheese and pepperoni pizza from​ Doug's Pizza Palace and felt there​ wasn't enough cheese and pepperoni on​ it, This led him to wonder what the average weight of a large cheese and pepperoni pizza was at​ Doug's Pizza Palace. Doug ordered a large cheese and pepperoni pizza from​ Doug's Pizza Palace on 15 randomly selected days during a particular term and weighed each before eating it. Suppose all conditions are met for inference using the​ one-sample t-methods. The student obtained the following​ 95% confidence interval​ (in grams) for the population​ mean, (862,1028). What is the value of the sample​ mean?

945 grams

The expression z Subscript alpha divided by 2zα/2 denotes the​ z-score with an area of​ _______ to its right.

α/2

Which of the following statements is true about a normal density curve as sigmaσ ​increases?

The height of the curve decreases.

Which of the following is a correct explanation of what a confidence interval​ is?

A confidence interval is a range of values used to estimate the true value of a population parameter. The confidence level is the probability the interval actually contains the population​ parameter, assuming that the estimation process is repeated a large number of times.

Identify which of the following is not a property of the Normal probability density function or state that they all are.

These are all properties of the Normal probability distribution.

Days before a presidential​ election, a nationwide random sample of registered voters was taken. Based on this random​ sample, it was reported that​ "52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus±​3%." The margin of error was based on a​ 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval.We are​ ___________ confident that the​ ___________ of registered voters​ ___________ planning on voting for Robert Smith is between​ ___________ and​ ___________.

We are 95% confident that the percentage of registered voters in the nation planning on voting for Robert Smith is between 49% and 55%.

What​ factor(s) affect the accuracy of the sample mean as an estimate of the population​ mean?

Sample size and variability

Since the area of the rectangle for a uniform probability distribution must equal​ one, what must the height​ equal, in​ general?

1/range

Complete the statement.A critical value is​ _____________.

A critical value is the number of standard errors​ (or standard​ deviations) to move from the mean of a sampling distribution to correspond to a specified level of confidence.

Which of the following is most likely to have a uniform probability​ distribution?

The random variable which records the numbers between 0 and 1 generated by a random number generator

Which of the following​ is/are correct interpretations of the area under the graph of a probability density function for any interval of values of the random​ variable?

Both of the statements in A and B are true.

t has often been suggested that students study 2 hours per week outside of class for every credit hour a class is worth. For​ example, students taking a 3 hour class are expected to study 6 hours for that class per week outside of class. A student wondered if her fellow classmates followed that guideline. She randomly sampled 100 students from her university and asked each to estimate the number of hours they studied outside of class each week​ (on average) that term and the number of credit hours they were taking that term. A​ 95% confidence interval for the average number of hours studied outside of class per week per credit hour taken for students at this university is​ (1.3,1.9). Based on this confidence​ interval, which of the following is​ true?

Because the bounds of the confidence interval are below​ 2, it does not appear that students at this university are studying the recommended 2 hours per week per credit​ hour, on average

If the area to the left of a​ z-score is less than​ 0.5, what must be​ true?

The​ z-score must be negative.

The larger the​ sample, the​ _______ accurate the sample mean will be as an estimate of the population mean.

moe

There were 100 random samples of the same size taken from a population which is known to have a normal distribution with some mean and a known standard deviation. A​ 95% confidence interval for the population mean was constructed for each of the 100 random samples. If all the conditions are​satisfied, what percentage of these confidence intervals would capture the true population​ mean?

Approximately​ 95% of them

A hungry college student just finished eating a large cheese and pepperoni pizza from​ Doug's Pizza Palace and felt there​ wasn't enough cheese and pepperoni on it as he has had large pizzas with more cheese and pepperoni on it from this place in the past. This led him to wonder what the average weight of a large cheese and pepperoni pizza was at​ Doug's Pizza Palace. Doug ordered a large cheese and pepperoni pizza from​ Doug's Pizza Palace on 15 randomly selected days during a particular term and weighed each before eating it. Suppose all conditions are met for inference using the​ one-sample t-methods. The student constructed a​ 95% confidence interval for the population mean using the​ one-sample t-methods. How many degrees of freedom does the t critical value​have?

14

Fill in the blank.To find the area between two​ z-scores on a​ calculator, use the​ _______ command.

normalcdf

What critical value should be used to construct a​ 90% confidence interval for the population mean when the population standard deviation is​ known?

z=1.645

Nurses wondered if birth weights of babies are going up. They knew that the average birth weight of a baby last year was 7.6 pounds. A random sample of 15 weights of babies at the hospital where the nurses work gave an average birth weight of 7.9 pounds. Nurses felt that the birth weights this year were normally distributed. Which of the following is true about the distribution of sample​ means?

Even though the sample size is less than​ 30, the distribution of sample means will be normal because the population data follow a normal distribution.

If you roll a fair die 100 times and construct a normal probability plot of the​ outcomes, what pattern would you expect in the​ graph?

Since the outcomes are not likely to have a normal​ distribution, the pattern of the points should not be a straight line pattern.

What is the purpose of constructing a normal probability​ plot?

A normal probability plot is used to determine if it is reasonable to assume that sample data are from a population having a normal distribution.

A hungry college student just finished eating a large cheese and pepperoni pizza from​ Doug's Pizza Palace and felt there​ wasn't enough cheese and pepperoni on it. This led him to wonder what the average weight of a large cheese and pepperoni pizza was at​ Doug's Pizza Palace. Doug ordered a large cheese and pepperoni pizza from​ Doug's Pizza Palace on 15 randomly selected days during a particular term and weighed each before eating it. Suppose all conditions are met for inference using the​ one-sample t-methods. The student obtained the following​ 95% confidence interval​ (in grams) for the population​ mean, (862,1028). What is the margin of​ error?

83 g

Researchers studied the mean egg length​ (in millimeters) for a bird population. After taking a random sample of​ eggs, they obtained a​ 95% confidence interval of​ (45,60). What is the value of the margin of​ error?

7.5 mm

If you select a simple random sample of​ 12-ounce pop cans and construct a normal probability plot of their​ weights, what pattern would you expect in the​ graph?

Since the weights are likely to have a normal​ distribution, the pattern of the points should be approximately a straight line.

Which of the following would increase the width of a confidence interval for a population​ mean?

Increase the level of confidence

Determine whether the graph can represent a Normal density function or explain why it cannot.

​No; this graph is not symmetric.

In a normal​ distribution, approximately​ 95% of the area under the normal curve is within how many standard​ deviation(s) of the​ mean?

Two

In a normal​ distribution, approximately​ 99.7% of the area under the normal curve is within how many standard​ deviation(s) of the​ mean?

three

In a continuous uniform probability​ distribution, what does the mean​ equal?

min+max/2

Birth weights in the United States are normally distributed with sigma Subscript x Baseline equals 500 grams.σx=500 grams. A random sample of 15 babies was taken. The average birth weight of these 15 babies was 3450 grams. Which of the following is true regarding the distribution of sample​ means?

The distribution of sample means will be normal since birth weights of all babies are normally distributed.

When working with normal probability​ plots, straight lines indicate​ _______ while curves represent​_______.

When working with normal probability​ plots, straight lines indicate normality while curves represent nonnormality.

In a normal​ distribution, approximately​ 68% of the area under the normal curve is within how many standard​ deviation(s) of the​ mean?

one

A graduate student wanted to estimate the average time spent studying among graduate students at her school. She randomly sampled graduate students from her school and obtained a​ 99% confidence interval of​ (17,25) hours/week. Which of the following would be true if the level of confidence was lowered to​ 95%?

The width of the confidence interval would be smaller

If the area under the standard normal curve to the left of zequals=minus−1.72 is​ 0.0427, then what is the area under the standard normal curve to the right of zequals=​1.72?

0.0427

The possible values that we believe a population mean will be with a certain level of confidence

form a confidence interval for the population mean.