Deck 6: Modeling Random Events: the Normal and Binomial Models

Question 1

The normal distribution below reflects a data set of gas consumption (in miles per gallon) for a group of trucks. The center is shown at 24 mpg and the standard deviation is 4 mpg. Choose the most accurate statement.

A)Approximately 68% of all of the trucks miles per gallon is between 20 and 28.
B)Approximately 99.7% of all of the trucks miles per gallon is between 12 and 36.
C)The top 2.5% of all of the trucks miles per gallon is greater than 32.
D)All of the above statements are accurate.

Answer 1

All of the above statements are accurate.

Question 2

Assume 80% of adults with arthritis symptoms report relief with a specific medication. If a new medication is given to 10 new patients with symptoms, what is the probability that the medication effectively relieves their symptoms? Select the most accurate statement to investigate the assumptions for using a binomial distribution model.

A)The outcome is relief from symptoms, yes or no with relief as a yes.
B)The probability of success for each new patient is 0.8.
C)It is reasonable to assume that the replications are independent.
D)All of the above assumptions are true.

Answer 2

All of the above assumptions are true.

Question 3

A data set of gas consumption for trucks (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a smaller spread of the normal distribution?

A)The standard deviation was 7.5 mpg.
B)The standard deviation was 2.5 mpg.
C)The center of the distribution would be greater than 24.8mpg.
D)The center of the distribution would be less than 24.8 mpg.

Answer 3

The standard deviation was 2.5 mpg.

Question 4

The normal model N (58, 21) describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z-score of -2.01. What is the weight of this egg in grams? Round to the nearest hundredth of a gram.

A)31.20 grams
B)15.79 grams
C)28.50 grams
D)38.10 grams

Question 5

Determine which of the given procedures describe a binomial distribution.

A)Record the number of songs downloaded in a month for a group of 30 randomly selected college students.
B)Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58.
C)Surveying customers entering a sporting equipment store until a customer responds that he or she was shopping for a bicycle.
D)Surveying every 5th person going into a department store to determine age groups of customers.

Question 6

Determine whether the variable would best be modeled as continuous or discrete: The temperature of a cup of coffee dispensed from a beverage vending machine, taken four times during a 24-hour period.

A)Continuous
B)Discrete

Question 7

Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or more said yes to this question? Why?

A)Yes, 45 would be an unusually small number of people given the known probability of 0.115.
B)No, 45 is within the expected range of people.
C)Yes, 45 would be an unusually large number of people given the known probability of 0.115.
D)Cannot be determined with the given information.

Question 8

Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

A)Approximately 95% of all Benneke brand canned peaches will weigh between 12.84 ounces and 14.16 ounces.
B)The probability that a randomly selected can of Benneke peaches will weigh between 12.9 ounces and 13.6 ounces is approximately 0.585.
C)About 4% of all cans of Benneke peaches will weigh less than 12.9 ounces
D)All of the above statements are true.

Question 9

Which of the following characteristics are not required for the binomial model?

A)The probability of success and of failure must be equal.
B)There are a fixed number of trials.
C)The trials must be independent.
D)The probability of success is the same at each trial.

Question 10

Use the following information to answer questions (3)-(4). A package delivery service divides their packages into
weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights
within that class are equally likely to occur. The probability density curve is shown below.
Find the probability that a package weighs between 14 and 18 pounds?

A)0.67
B)0.33
C)0.40
D)0.80

Question 11

Use the following information to answer questions .
Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x
value.
What is the approximate probability that x = more than 10? Round to the nearest hundredth place.

A)0.20
B)0.10
C)0.02
D)0.88

Question 12

Use the following information for following questions . The average travel time to work for a person living and
working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and
the distribution of travel time is approximately normally distributed.
What is the travel time to work that separates the bottom 2.5% of people with the median or 50%? Round to the nearest tenth of a minute.

A)7 to 17 minutes
B)3.5 to 17 minutes
C)8 to 17 minutes
D)12.5 to 17 minutes

Question 13

Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24-hour period.

A)Continuous
B)Discrete

Question 14

Use the following information to answer questions (3)-(4). A package delivery service divides their packages into
weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights
within that class are equally likely to occur. The probability density curve is shown below.
Find the probability that a package weighs less than 20 pounds?

A)0.80
B)0.40
C)1.00
D)0.20

Question 15

Use the following information to answer questions .
Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x
value.
What is the approximate probability that x = 6 or less? Round to nearest hundredth place.

A)0.44
B)0.56
C)0.13
D)0.76

Question 16

Use the following information for following questions . The average travel time to work for a person living and
working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and
the distribution of travel time is approximately normally distributed.
Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 12.5 minutes? Round to the nearest whole percent.

A)16%
B)68%
C)5%
D)84%.

Question 17

Use the following information for following questions . A box contains recipes from five categories. The following table
shows the possible categories and the associated probability for a recipe randomly chosen.
What is the probability of randomly selecting anything but a vegetable or main dish category? Round to the nearest tenth of a percent.

A)4.9%
B)48.6%.
C)51.4%
D)5.1%

Question 18

Use the following information for following questions . A box contains recipes from five categories. The following table
shows the possible categories and the associated probability for a recipe randomly chosen.
What is the probability of randomly selecting either an appetizer or salad category? Round to the nearest tenth of a percent.

A)3.7%
B)61.7%.
C)3.8%
D)38.3%

Question 19

Use the following information for following questions . Male players at the high school, college and professional
ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the
weights of basketballs are approximately normally distributed.
Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to the nearest tenth of a percent.

A)Roughly 15.1% of the basketballs will weigh more than 23.1 ounces.
B)Roughly 42.3% of the basketballs will weigh more than 23.1 ounces.
C)Roughly 36.4% of the basketballs will weigh more than 23.1 ounces.
D)Roughly 13.6% of the basketballs will weigh more than 23.1 ounces.

Question 20

Use the following information for following questions . Male players at the high school, college and professional
ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the
weights of basketballs are approximately normally distributed.
If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth.

A)0.547
B)0.315
C)0.685
D)0.723

Question 21

Use the following information for following questions . The Normal distribution below models the distribution of
highway gas consumption (in miles per gallon) for a large collection of SUVs when driving on level roads. The
center is shown at 24.8 mpg and the standard deviations reflect the spread of the data.
Choose the most accurate statement.

A)The top 5% of SUVs get 37.2 mpg or higher.
B)The top 2.5% of SUVs get 37.2 mpg or higher.
C)The bottom 32% of SUVs get 18.6 mpg or lower.
D)The bottom 0.3% of SUVs get 6.2 mpg or lower.

Question 22

Determine whether the variable would best be modeled as continuous or discrete: The amount of time it takes students to get to school.

A)Continuous
B)Discrete

Question 23

Admission to a certain university is determined by an entry exam. The scores of this test are Normally distributed with a mean of 400 and a standard deviation of 60. Only students who score in the top 30% will be offered admission. Amy scores 425 on the test. Choose the most accurate statement.

A)The top 30% is defined with a score less than or equal to 431.4 so she will be admitted.
B)The top 30% is defined with a score greater than or equal to 431.4 so she will not be admitted.
C)The top 30% of all students have scores greater than or equal to 520 so she will not be admitted.
D)The top 30% of all students have scores greater than or equal to 460 so she will not be admitted.

Question 24

Use the following information to answer questions . A package delivery service divides their packages into
weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights
within that class are equally likely to occur. The probability density curve is shown below.
Find the probability that a randomly selected package will weigh less than 18 pounds.

A)0.67
B)0.80
C)0.20
D)0.30

Question 25

A summary of the types of movies showing in a small city, contains five genres. The following table shows the genres and the associated probability for that type of movie available on a particular weekend. The table is a probability distribution. If we chose a theater and movie to attend at random, what probability would we have of seeing anything other than a romantic or sci-fi movie?

A)0.646
B)0.677
C)0.880
D)0.323

Question 26

Use the following information for following questions . The mean time it takes for workers at a factory to insert a
delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the
distribution of time is approximately normally distributed.
For a randomly selected worker, what's the approximate probability the bolt will be inserted in 19 minutes or less? Round to the nearest whole percent.

A)50%
B)84%
C)18%
D)16%

Question 27

Use the following information for following questions . A police radar gun is used to measure the speeds of cars on a
highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5
mi/hr.
Roughly what proportion of cars are driving between 60 and 70 mi/hr? Round to the nearest thousandth)

A)0.157
B)0.843
C)0.314
D)0.628

Question 28

Use the following information to answer questions .
What is the approximate probability that x is equal to more than 10? Round to the nearest hundredth place.

A)0.20
B)0.10
C)0.02
D)0.88

Question 29

Determine which of the given procedures describe a binomial distribution.

A)The number of tattoos in a group of 30 randomly selected college students.
B)The number out of the next ten customers at a hotdog stand order who order onions, assuming that each has the same probability of ordering onions.
C)The number of customers surveyed, while leaving a grocery store, until a customer responds that he or she spent more than fifty dollars.
D)The ages of every 5th person entering a department store.

Question 30

Determine whether the variable would best be modeled as continuous or discrete: The number of tails when flipping ten coins.

A)Continuous
B)Discrete

Question 31

Use the following information to answer questions .
What is the approximate probability that x is equal to 5 or less? Round to nearest hundredth place.

A)0.29
B)0.13
C)0.17
D)0.71

Question 32

The distribution of gas consumption for SUVs driving on flat highways is approximately Normal with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a larger spread of the normal distribution?

A)The standard deviation was 7.5 mpg.
B)The standard deviation was 2.5 mpg.
C)The center of the distribution is greater than 24.8 mpg.
D)The center of the distribution is less than 24.8 mpg.

Question 33

Use the following information for following questions . The Normal distribution below models the distribution of
highway gas consumption (in miles per gallon) for a large collection of SUVs when driving on level roads. The
center is shown at 24.8 mpg and the standard deviations reflect the spread of the data.
Choose the most accurate statement.

A)Approximately 95% of all SUVs have gas consumption between 12.4 and 37.2 mpg.
B)Approximately 99.7% of all SUVs have gas consumption between 12.4 and 37.2 mpg.
C)The top 25% of gas consumption of SUVs is greater than 31.0 mpg.
D)The bottom 30% gas consumption of all SUVs is less than 18.6 mpg.

Question 34

Use the following information for following questions . The Normal distribution below models the distribution of
highway gas consumption (in miles per gallon) for a large collection of SUVs when driving on level roads. The
center is shown at 24.8 mpg and the standard deviations reflect the spread of the data.
What percent of SUVs consume 37.2 mpg or less?

A)90%.
B)97.5%
C)95%.
D)50%.

Question 35

The distribution of gas consumption for SUVs (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. A similar data set for a group of sedans is approximately normally distributed with a center of 28 mpg and a standard deviation of 4 mpg. Which one of the following statements is true when the distributions are compared on a number line?

A)The normal distribution for the sedans is shifted to the right and not as spread out.
B)The normal distribution for the SUVs is centered at the same value as for the sedans but spreads out further.
C)The normal distribution for the sedans is shifted to the right and more spread out.
D)The normal distribution of the SUVs is centered at the same value as for the sedans but does not spread out as far.

Question 36

Some statisticians use a guideline that says that events that happen 5% of the time or less often should be considered "unusual." By this standard, is it unusual to have a car speed of 75 mi/hr or greater?

A)No, this would not be unusual because it is only 2 standard deviations higher than the mean.
B)No, this would not be unusual because is only 1 standard deviation higher than the mean.
C)Yes, this would be unusual because it is 3 standard deviations higher than the mean.
D)Yes, this would be unusual because it is 4 standard deviations higher than the mean.

Question 37

Can the following problem be solved by using a binomial model? Let's say that the probability that a student will arrive on time for a statistics class is 70%. How many students out of 30 would be on time for the last day of class?

A)This problem can be solved using the binomial model because the students are not independent.
B)Not enough information is provided to determine if the binomial model can be used.
C)This problem cannot be solved using the binomial model because the students are not independent.
D)A binomial model is only valid for the average probability rather than a particular day's probability.

Question 38

Use the following information for following questions . The mean time it takes for workers at a factory to insert a
delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the
distribution of time is approximately normally distributed.
97.5% of the time, the bolt is inserted in less than which time value? Round to the nearest whole number.

A)23 minutes
B)19 minutes
C)7 minutes
D)15 minutes

Question 39

Use the following information for following questions . A police radar gun is used to measure the speeds of cars on a
highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5
mi/hr.
Roughly what percentage of cars are driving less than 45 mi/hr? (Round to the nearest tenth of a percent)

A)5.0%
B)95.0%
C)18.0%
D)2.5%.

Question 40

Use the following information to answer questions . A package delivery service divides their packages into
weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights
within that class are equally likely to occur. The probability density curve is shown below.
Find the probability that a randomly selected package will weigh between 16 and 18 pounds.

A)0.80
B)3.60
C)0.33
D)0.20