# MAT 1450 Exam 2

25 Questions

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• 1.
The law of large number states that as the number of observations drawn at random from a population (with finite mean μ) increases, the mean x of the observed values
• A.

Gets larger and larger

• B.

Gets smaller and smaller

• C.

Tends to get closer and closer to the population mean μ

• D.

Fluctuates steadily between 1 standard deviation above and below μ

• 2.
A public opinion poll wants to determine whether registered voters in Ohio approve of a measure to ban smoking in all public areas. the researchers select a random sample of 50 registered voters from each country in the state and ask whether they approve or disapprove of the measure. this is an example of:
• A.

A systematic county sample

• B.

A stratified sample

• C.

A multistage sample

• D.

A simple random sample

• 3.
A news release for a diet product company reports: "there's good news from the 65 million Americans currently on a diet." it's own study showed that people who lose weight can keep it off. the sample was 20 graduates of the company's program who endorsed the program in commercials. the results of the sample are probably
• A.

Biased, overstating the effectiveness of the diet

• B.

Biased, understanding the effectiveness of the diet.

• C.

Unbiased since the people in the sample are nationally recognized individuals

• D.

Unbiased, but they could be more accurate. a larger sample size should be used.

• 4.
The density curve for a continuous random variable X has which of the following properties?
• A.

The probability of any event (pi) must be 0 ≤ pi ≤ 1

• B.

The total area under the density curve for X must be exactly 1

• C.

The probability of any event of the form X = Constant is 0

• D.

All of the above

• 5.
The most important condition for sound conclusions from statistical interference is usually
• A.

That the data can be thought of as a random sample from the population of interest

• B.

That the population distribution is exactly normal

• C.

That the data contain no outliars

• 6.
A survey of senior citizens finds that 80% have a landline telephone, 36% have a cell phone, and 24% have both a landline and a cell phone. What is the proportion of senior citizens who have a cell phone but not a landline?
• 7.
A survey of senior citizens finds that 80% have a landline telephone, 36% have a cell phone, and 24% have both a landline and a cell phone. What is the proportion of senior citizens who have neither a cell phone nor a landline?
• 8.
A survey of senior citizens finds that 80% have a landline telephone, 36% have a cell phone, and 24% have both a landline and a cell phone. What is the proportion of senior citizens who have either a cell phone or a landline?
• 9.
A survey of senior citizens finds that 80% have a landline telephone, 36% have a cell phone, and 24% have both a landline and a cell phone. What is the conditional probability a senior citizen has a cell phone given that (s)he has a landline phone?
• 10.
This table gives the sex and age group of library card holders. a library card hoder is to be selected at random. What is the probability that a randomly selected library card holder is 16 to 24 years old?
• 11.
This table gives the sex and age group of library card holders. a library card holder is to be selected at random. What is the probability that a randomly selected library card holder is a female?
• 12.
This table gives the sex and age group of library card holders. a library card holder is to be selected at random. Given that the randomly selected library card holder is between age 25 and 34, what is the probability that card holder is a male?
• 13.
Each month, the U.S. census bureau mails survey forms to 250,000 randomly selected households asking questions about the people living in the household and about such things as motor vehicles and housing costs. Telephone calls are made to households that don't return the form. In one month, responses were obtained from 238,000 of the households contacted.
• A. What is the sample in the situation?
• A.
• B. What is the population in this situation?
• B.
• 14.
To assess the opinion of students at the Ohio State University about campus safety, a reporter for the student newspaper interviews 12 students she meets walking on the campus late at night who are willing to give their opinion.
• A. What is the sample for this scenario?
• A.
• B. What is the method of sampling used for this scenario?
• B.
• 15.
In a national survey of sleeping habits, 10,000 adults were selected randomly and contacted by telephone. Respondents were asked, "Typically, how many times per week do you sleep more than 6 hours during the night?" Those surveyed reported an average of 5.2 nights per week in which they got more than 6 hours of sleep. The standard deviation of the sample is calculated as s = 0.85 per week.
• A. Identify a numeric value that is a stistic which represents and estimate of an unknown parameter
• A.
• B. What is the sample size of this scenario?
• B.
• C. What does the theory tell us the value of σ (population standard deviation) will be?
• C.
• 16.
The probability density of a random variable X is given in the following figure. From this density, what is the probability that X is between 0.5 and 1.5?
• 17.
The probability density of a random variable X is given in the following figure. From this density, what is the probability that X is at least 0.5?
• 18.
The probability density of a random variable X is given in the following figure. From this density, what is the probability that X is 2.5?
• 19.
Suppose that the blood cholesterol level of all US women aged 20 to 34 follows the Normal distribution with a mean μ = 185 milligrams per deciliter (mg/dl) and standard deviation σ = 39 mg/dl. What proportion of women in the 20 to 34 age range have cholesterol levels that are less than 253?
• 20.
Suppose that the blood cholesterol level of all US women aged 20 to 34 follows the Normal distribution with a mean μ = 185 milligrams per deciliter (mg/dl) and standard deviation σ = 39 mg/dl. What is the probability a randomly selected woman will have a cholesterol level that is more than 225 mg/dl?
• 21.
Suppose that the blood cholesterol level of all US women aged 20 to 34 follows the Normal distribution with a mean μ = 185 milligrams per deciliter (mg/dl) and standard deviation σ = 39 mg/dl. If a SRS of 36 women is chosen from this population. what is the sampling distribution of x?
• 22.
Suppose that the blood cholesterol level of all US women aged 20 to 34 follows the Normal distribution with a mean μ = 185 milligrams per deciliter (mg/dl) and standard deviation σ = 39 mg/dl. If a SRS of 1000 women is chosen from this population, what is the sampling distribution of x?
• 23.
Suppose that the number of close friends adults claim to have varies from person to person with mean σ = 2.5. an opinion poll asks this question for an SRS of 1500 adults. In this situation the sample mean response x has approximately the Normal distribution with mean 9 and standard deviation of 0.075. What is P (8.8 ≤ x ≤ 9.2), the probability that the sample results x estimates the population truth σ = 9 to within ±0.2? Round your answer to 3 decimal places.
• 24.
Suppose that the number of close friends adults claim to have varies from person to person with mean σ = 2.5. an opinion poll asks this question for an SRS of 1500 adults. In this situation the sample mean response x has approximately the Normal distribution with mean 9 and standard deviation of 0.075. What is P (x ≥ 10), the probability that the sample result x is greater than 10? Round your answer to 3 decimal places.
• 25.
In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 pounds in teh summer, including clothing and carry-on baggage. but passengers vary, and the FAA did not specify a standard deviation. a reasonable standard deviation is 35 pounds. weights are not Normally distributed, especially when the population includes both men and women, but they are close to Normal. A commuter plane carries 25 passengers. approximate the probability that the total weight of the passengers exceeds 4400 pounds.
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