Midterm Exam 2

A credit card company issues a credit card to a person for whom there is a likelihood of 0.8 that he will borrow on the card and pay a steady flow of interest of $24 per month, and a likelihood of 0.2 that he will pay all his borrowings promptly and incur no interest. What is the expected flow of interest payments to the company?

$19.20 per month

An insurance company knows that the average cost to build a home in a new California subdivision is $100,000 and that in any particular year there is a 1 in 50 chance of a wildfire destroying all the homes in the subdivision. Based on these data and assuming the insurance company wants a positive expected value when it sells policies, what is the minimum that the company must charge for fire insurance policies in this subdivision?

$2000 per year

Before you church plant in Holbrook, AZ, you wish to look at the A/V expenses of other churches in the community to get a grasp on what to expect. The expenditures of six local churches are $2,100; $204,700; $41,160; $15,920; $36,030; and $52,870. What is the range for this data set?

$202,600

One in 100 tennis balls produced at a factory is defective. If you randomly select five tennis balls, what is the probability that at least one will be defective?

1 - 0.99^5

You are playing 5-card poker with a deck of 52 cards. If you could make a probability distribution showing the individual probabilities of all possible hands, the sum of all the individual probabilities would be

1.

A mail-order catalog lists products using a catalog number consisting of four numerical digits followed by three letters of the alphabet. How many different catalogue numbers are possible?

10 x 10 x 10 x 10 x 26 x 26 x 26

You roll two dice. Based on the probabilities shown in the table below, what is the probability that you'll get a sum of 3 on the first roll and a sum of 4 on the second roll? (See the Graph)

2/36 x 3/36

Assuming the previous problem's distribution is normal, approximately what percent of sermons go longer than yours?

4%

Your church's statistician calculates (from previous weeks' data) the following in regards to the probability of second service attendance: 20% chance of 350 people 25% chance of 375 people 35% chance of 410 people 20% chance of 500 people What is the expected number of people whom will attend your church's second service?

408 people

According to the graph, what was the percentage of Christians in Saudi Arabia in 2000, roughly speaking? (See the Graph)

5%

You are training for a mile race and have been practicing daily for the big day. Below is the data set for your mile times in minutes: 5.92, 6.16, 6.29, 5.87, 6.13, 5.95, 6.02, 5.99, 6.04 What is the median time for this data set?

6.02 minutes

In a normal curve, roughly _______ of the mass is within two standard deviations of the distribution's mean.

95%

Why is this graph misleading? (TV Size Comparison)

A perceptual distortion is taking place.

The graph below is a good example of a __________ distribution. (See the Graph)

A. bimodal uniform

The events of being born on a Wednesday and being born in July are

A. overlapping. mutually exclusive.

If an airline is caught with the negative consequences of overbooking, they are often forced to reimburse the additional passengers and thus lose out on potential business in the future. Using the standard deviation calculated in the previous problem and assuming a normal distribution, which best describes the likelihood this airline would have have to reimburse some of its passengers for its mistake in overbooking? (Hint: How likely is it that over 215 passengers show on a given day?)

About 2.5% or Highly unlikely, less than 0.15%

What type of statistical study is most likely to lead to an answer to the question, "Does Fortify! garden fertilizer produce larger tomatoes?"

An experiment

What type of statistical study is most likely to lead to an answer to the question, "Which state in the U.S. has the largest percentage of Christians?"

An observational study

A survey is conducted to see what percentage of the city is Christian. To carry out the survey, individuals are asked directly at the entrance of the local beach. This is a prime example of

Convenience sampling.

At Calvary Chapel Bible College, a poll was taken to see which translation was the most common among the students. In a sample of 200 CCBC students, 36 preferred ESV, 20 preferred NIV, 89 preferred NKJV, and 55 preferred KJV. Which translation was the mode of this data set?

NKJV

Which best describes the relationship between an individual's reputation and their character?

Reputation is positively correlated with character.

Airlines often overbook flight seating knowing not all passengers will show up on the day of their travel. An airline has been selling 220 flight tickets for a plane that can hold 215 passengers. On average, however, the airline typically sees a mean of 210 passengers who actually fulfill their purchased ticket. During the last three days, the plane has had 209, 212, and 210 passengers respectively. Using 210 passengers as the mean amount of passengers, what is the standard deviation for this data set?

SD = 1.73 passengers SD = 1.58 passengers

A computer randomly selects 400 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for mayor. What type of sampling method is being applied?

Simple Random Sampling

An IRS auditor randomly selects for audits 30 taxpayers in each of the filing status categories: single, head of household, married filing jointly, and married filing separately. What type of sampling method is being used?

Stratified Sampling

You want to determine the typical dietary habits of students at CCBC. Which of the following would make the best sample?

Students found in the cafeteria from 11:00 AM to 1:00 PM

Suppose a person who has a habit of driving fast has never had a traffic citation. What does it mean to say that the "law of averages [large numbers] will catch up with him"?

The phrase means that over the long run, the person will most likely get a traffic citation.

Why is this graph misleading? (Pie Chart)

The relative frequencies don't add up correctly.

Why is this graph misleading? (Side by Side Bar Graph)

The scaling between graphs is inconsistent and deceptive.

Why is this graph misleading? (Bar Graph)

The scaling is too zoomed in and deceptive.

On a roll of two dice, Paul bets that the sum will be 5, and Timothy bets that the sum will be 8. Who has a higher probability of winning?

Timothy

According to the graph, roughly how much larger is the death rate for Christians compared to Muslims? (See the Graph)

Twice

A hijacked plane may land in Greece. It may also land in Cuba. Are these events mutually exclusive? Why or why not?

Yes, because the plane can only land in one place.

In California, a part-time employee is often required to average no more than 29 hours per week at the end of the year (an equivalent of 52 weeks). Since January 1st, you have worked 38 weeks at the Conference Center and currently have an average 32 hours per week. Thus, because of the labor law definition for a part-time worker, your boss tells you that for the remaining 14 weeks left in the year, you will need to reduce your hours so that in 14 weeks your average goes down to 29 hours per week. If you work only 20 hours per week until December 31, will you meet your boss' request? (Hint: Find the total number of hours this would mean for the entire year and then finish by dividing by 52 weeks).

Yes, your end of the year average will be slightly below 29 hours per week.

If the points on a scatterplot fall into a broad swath that slopes downward, the two variables have

a weak correlation or no correlation

A study at the University of Southern California separated 108 volunteers into groups, based on psychological tests designed to determine how often they lied and cheated. Those with a tendency to lie had different brain structures than those who did not lie (British Journal of Psychiatry). This is an example of an

affected data report

In order to gauge church opinion on how Christians in the United States view abortion, the Pew Research Center surveyed 1000 American Christians by telephone. In the following study, what is the population?

all Christians in the United States

Which best describes the distribution for a restaurant's business throughout the day?

bimodal

A Gallup poll of 1051 American adults shows that 32% of Americans say they have been spending less in recent months and 27% say they are saving more now and intend to make this their new, normal pattern in the years ahead. What is this study's sample statistic?

both are sample statistics

When you toss one coin, the probability that you'll get heads is 1/2. Assuming the coin is fair, this means that

if you toss 1000 coins, there's no way to predict the precise number of heads you'll get, though it will probably be close to 500.

The distribution below is... (See the Graph)

left-skewed.

Using a survey of 35,000 Americans, the Pew Forum on Religion and Public Life determined that between 47 and 59 percent of adults switch their religious/faith affiliation at least once in their lives. This is an example of an

observational study.

The following is an example of a

pie chart

You carry out a study and find the data characteristics of someone's gender, eye color, hair color, and favorite foods. The characteristics described here are examples of

qualitative data.

The number of hours someone prays daily, a church's weekly attendance, and the amount of NKJV bibles in the U.S. are all prime examples of

quantitative data.

The ____________________ measures how far data values are spread around the mean of a data set and is in essence a measure of the average of all deviations from the mean.

standard deviation

The distribution of teeth loss (natural) during someone's lifetime is best described as

symmetric or asymmetric

An AP/CBS telephone poll of 998 randomly selected Americans revealed that 6 in 10 people believe there has been progress in finding a cure for cancer in the last 30 years. What is the sample in this study?

the 998 randomly selected Americans

In a USA Today/Gallup poll of 1027 Americans surveyed by cell phones and land lines, 62% of those who responded said that they believed in an afterlife. In this study, what is the population parameter?

the percentage of Americans who believe an afterlife exists

When can you rule out the possibility that changes to variable X cause changes to variable Y?

when there is no correlation between X and Y

According to Pew Research Institute, the average (mean) evangelical Sunday morning sermon teaching lasts 36 minutes with a standard deviation of roughly 8 minutes. If your previous sermon lasted 50 minutes, what is the z-score for this data point?

z = 1.75 minutes