MML STATS
Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 10 main dishes, 9 vegetable dishes, and 12 desserts. How many different meals are possible?
10 times 9 times 12C2
You have 12 different video games. How many different ways can you arrange the games side by side on a shelf?
12! on calc
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage? (C.) What is a disadvantage of using the range as a measure of variation?
It uses only two entries from the data set.
What is a discrete probability distribution? Choose the correct answer below.
A discrete probability distribution lists each possible value a random variable can assume, together with its probability.
how is a sample related to a population
A sample is a subset of a population.
In a poll, 1,003 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 48% said that they were in favor. Describe the statistical study. A.) what is the population in the given problem?
All men in the country
What is the difference between an outcome and an event?
An outcome is the result of a single probability experiment. An event is a set of one or more possible outcomes.
Which method of data collection should be used to collect data for the following study. Upper A study of the health of 174 lung transplant patients at a hospital.
Census
Researchers found that people with depression are seven times more likely to have a breathing-related sleep disorder than people who are not depressed. Identify the two events described in the study. Do the results indicate that the events are independent or dependent? Are the events independent or dependent?
Dependent
Researchers found that people with depression are seven times more likely to have a breathing-related sleep disorder than people who are not depressed. Identify the two events described in the study. Do the results indicate that the events are independent or dependent? Identify the two events. Choose the correct answer below.
Depression and breathing-related sleep disorder
(b) List an example of two events that are dependent. Choose the correct answer below.
Drawing one card from a standard deck, not replacing it, and then selecting another card
Describe the difference between the value of x in a binomial distribution and in a geometric distribution.
In a binomial distribution, the value of x represents the number of successes in n trials, while in a geometric distribution, the value of x represents the first trial that results in a success.
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage? B.) What is an advantage of using the range as a measure of variation?
It is easy to compute.
In a binomial experiement, what does it mean to say that each trial is independent of the other trials?
Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials.
determine whether the survey question is biased. If the question is biased, suggest a better wording. Why is eating cake bad for you? B.) If the question is biased, which question below is worded better?
How do you think eating cake affects your health
Determine whether the data set is a population or a sample. Explain your reasoning. The age of each member of the House of Representatives.
Population, because it is a collection of ages for all members of the House of Representatives.
Determine whether the data set is a population or a sample. Explain your reasoning. The age of each resident in an apartment building.
Population, because it is a collection of ages for all people in the apartment building.
Use the box-and-whisker plot to identify (a) the five-number summary, and (b) the interquartile range. IQR= ?
Q3-Q1
Determine whether the variable is qualitative or quantitative. Number of words in a speech
Quantitative
Determine whether the variable is qualitative or quantitative. Amount of sugar in a bag of sugar
Quantitative
What is the difference between relative frequency and cumulative frequency?
Relative frequency of a class is the percentage of the data that falls in that class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.
(a) List an example of two events that are independent. Choose the correct answer below.
Rolling a die twice
Sony wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 90 customers and asks them about their level of satisfaction with the company.
Simple random
How is a Pareto chart different from a standard vertical bar graph?
The bars are positioned in order of decreasing height with the tallest bar on the left.
When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting?
The number of ordered arrangements of n objects taken r at a time.
Determine whether the statement is true or false. If it is false rewrite it as a true statement A data set can have the same mean, median, and mode.
the statement is true
The probability of randomly choosing a tea drinker who has a college degree (Assume that you are choosing from the population of all tea drinkers.)
The probability of choosing a tea drinker who does not have a college degree
What are the two conditions that determine a probability distribution? Choose the correct answer below.
The probability of each value of the discrete random variable is between 0 and 1, inclusive, and the sum of all the probabilities is 1.
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage? a.) Explain how to find the range of a data set. Choose the correct answer below.
The range is found by subtracting the minimum data entry from the maximum data entry.
A student's score on an actuarial exam is in the 78th percentile. What can you conclude about the student's exam score?
The student scored higher than 78% of the students who took the actuarial exam.
Compare the three data sets on the right (b) How are the data sets the same? How do they differ?
The three data sets have the same mean but have different standard deviations.
Suppose a survey of 555 women in the United States found that more than 67% are the primary investor in their household. (B.) Choose the best inference from the given information.
There is an association between U.S. women and being the primary investor in their household.
If two events are mutually exclusive, why is Upper P left parenthesis Upper A and Upper B right parenthesis equals 0?
Upper P left parenthesis Upper A and Upper B right parenthesis equals 0 because A and B cannot occur at the same time
What is the difference between a random sample and a simple random sample?
With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.
n a survey, travelers were asked to name what they found most annoying on a flight. One of the most common results was "crying kids." You randomly select six people who participated in the survey and ask them to name what they find most annoying on a flight. Let x represent the number who name crying kids as the most annoying. The random variable x has a binomial distribution, as shown to the right, with n=6 and p=0.36. Find the mean and standard deviation of this binomial distribution and interpret the results in the context of real life. What values of x would you consider unusual? Explain your reasoning. a. what is mean b. what is standard deviation c. fill in the blank d. fill in the blank
a. multiply two numbers given b. multiply two numbers given and 1-p c. mean mean standard deviation d. 5 and 6 // highly unlikely
Find the indicated probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities. A newspaper finds that the mean number of typographical errors per page is eight. Find the probability that (a) exactly five typographical errors are found on a page, (b) at most five typographical errors are found on a page, and (c) more than five typographical errors are found on a page.
a. poissonpdf (8,5) b. poissonCdf (8,5) c. 1-b d. none of the events are unusual
An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect. (a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 6000 cars. (b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p. Repeat (a) using a Poisson distribution and compare the results.
a.) binomialpdf
About 20% of babies born with a certain ailment recover fully. A hospital is caring for seven babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. a) Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. b.) What is a success in this experiment? c.) Specify the value of n. Select the correct choice below and fill in any answer boxes in your choice. d.) Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice. e.)Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. f.) List the possible values of the random variable x.
a.) yes b.) baby recovers c.) number of babies in hospital d.) percent given in decimal form e.) 100-.(percentage given) f.) x= 0,1,2,3,..., Highest number given
Find the range, mean, variance, and standard deviation of the sample data set. (B.) find the mean (explain)
add all of them up and divide by number of #s
Use the frequency histogram to answer each question. A.) Determine the number of classes (explain)
count the number of bars in the graph
Use the box-and-whisker plot to identify (a) the five-number summary, and (b) the interquartile range. Q1= ?
far left dot of box
Use the box-and-whisker plot to identify (a) the five-number summary, and (b) the interquartile range. Q3= ?
far right dot of box
Use the frequency histogram to answer each question. (d.) determine the class width
find the difference between two consecutive numbers given on the x-axis
The heights (in inches) of 20 female students in a physical education class are shown below. Approximate the mean height of students in a class. (explain)
find the midpoint of each number, multiply it by the frequency given and divide by the added up frequencies
Use the frequency histogram to answer each question. B.) estimate the frequency of the class with the least frequency (explain)
find the smallest class given and then see how tall it is on the graph
Use the frequency histogram to answer each question. (C.) estimate the frequency of the class with the greatest frequency
find the tallest class given and then see how tall it is on the graph
How many different simple random samples of size 4 can be obtained from a population whose size is 45?
last number given C first number given
Use technology to organize the data as a stem-and-leaf plot to display the data. The data represent the heights of eruptions by a geyser. What can you conclude about the data? A.) Chose the correct stem-and-leaf plot
look at the numbers given and match them up to the numbers in the graph
Compare the three data sets on the right (a) Which data set has the greatest sample standard deviation?
look for the one that is widest
Compare the three data sets on the right Which data set has the least sample standard deviation?
look for the thinnest one
Use the box-and-whisker plot to identify (a) the five-number summary, and (b) the interquartile range. Q2=?
middle dot of box
A software company is hiring for two positions: a software development engineer and a sales operations manager. How many ways can these positions be filled if there are 10 people applying for the engineering position and 13 people applying for the managerial position?
multiply the two numbers given
Suppose 70% of kids who visit a doctor have a fever, and 40% of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat?
multiply two numbers as decimals
A person lives in a household with three dogs and claims that having three dogs is not unusual. Using the frequency distribution below, determine if this person is correct.
no
Event A: Randomly selecting a nurse Event B: Randomly selecting a male Are the two events mutually exclusive?
no, because someone who is a nurse can be male
Use the pie chart at the right, which shows the number of tulips purchased from a nursery. Find the probability that a tulip bulb chosen at random is red
number given for red section / 100
Consider a company that selects employees for random drug tests. The company uses a computer to randomly select employee numbers that range from 1 to 5801. Find the probability of selecting a number less than 1000. Find the probability of selecting a number greater than 1000.
number of outcomes in event E (999)/ (5801)total number of outcomes in sample space
The graph to the right shows the responses to the question, "Does global warming contribute to El Nino? " Identify the level of measurement of the data listed on the horizontal axis in the graph. Data listed-- A: very likely B: somewhat likely C: Somewhat unlikely D: Very unlikely E. Unsure
ordinal
Select all the levels of measurement for which data can be qualitative.
ordinal, nominal
Determine whether the underlined value is a parameter or a statistic. A study of 6, 076 adults in public rest rooms found that 23 % did not wash their hands before exiting.
statistic
Find the range, mean, variance, and standard deviation of the sample data set. (C.) find the variance (explain)
subtract the mean from each number square the result, find the mean of all your new numbers
Find the range, mean, variance, and standard deviation of the sample data set. (d.) find the standard deviation (explain.)
take the square root of your variance
In a poll, 1,003 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 48% said that they were in favor. Describe the statistical study. Identify the sample for the given problem. Choose the correct answer below
the 1,003 men selected
Find the range, mean, variance, and standard deviation of the sample data set. (a) find the range (explain)
the biggest number minus the smallest
The measure of position called the midquartile of a data set is found using the formula StartFraction Upper Q 1 + Q 3 / 2 . Find the midquartile of the given data set
the half humber of the first half=Q1 the half number of the second half +Q3
Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why. The typing speeds (in words per minute) for several stenographers are listed below. (A.) Does the median represent the center of the data?
the median represents the center
Use the box-and-whisker plot to identify (a) the five-number summary, and (b) the interquartile range. min= ?
the minimum is the number at the far left dot
Use the box-and-whisker plot to identify (a) the five-number summary, and (b) the interquartile range. max=?
the number at the far right dot
Six of the 50 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?
the number of outcomes in event E (50-6) /(50) total number of outcomes in the sample space
A lottery is used to determine which team gets the first pick in its annual draft. The number of combinations assigned to each of the 7 teams is shown in the Pareto chart to the right. For each team, find the probability that the team will win the first pick.
the number on top of the bar divided by 1000
Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why. The typing speeds (in words per minute) for several stenographers are listed below. What is the mode of the typing speeds? Select the correct choice below and fill in any answer box to complete your choice. (explain)
which ever number appears the most
Use the Row of numbers shown below to generate 12 random numbers between 01 and 99 (explain process)
write 2 digit numbers in order of appearance in the line of numbers
Determine whether the survey question is biased. If the question is biased, suggest a better wording. Why is eating cake bad for you? A.) Is this question Biased
yes
Suppose a survey of 555 women in the United States found that more than 67% are the primary investor in their household. (A.) Choose the best statement of the descriptive statistic in the problem.
67% of women in the sample are the primary investor in their household
