Category:
Mathematics

Question 1 of 25 1.0 Points

Since the population is always larger than the sample, the population mean:

A. is always smaller than or equal to the sample mean

B. is always larger than or equal to the sample mean

C. can be smaller than, or larger than, or equal to the sample mean

D. is always strictly less than the sample mean

Question 2 of 25 1.0 Points

What is the probability of drawing two queens in a row from a standard deck of cards without replacement?

A. 0.0045

B. 0.0059

C. 0.0015

D. 0.0385

Question 3 of 25 1.0 Points

If one tosses a coin enough times, the proportion of “heads” will approach 0.5. This is an example of:

A. the Law of Large Numbers

B. subjective probabilities

C. the Empirical Rule

D. the Central Limit Theorem

Question 4 of 25 1.0 Points

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that fewer than 40 batteries will last at least 8 hours?

A. 0.7986

B. 0.0789

C. 0.9598

D. 0.9211

Question 5 of 25 1.0 Points

Which term is NOT synonymous with the expected value of a discrete probability distribution?

A. μ

B. mean

C. theoretical average

D. variance

Question 6 of 25 1.0 Points

A discrete probability distribution:

A. lists all of the possible values of the random variable and their corresponding probabilities

B. can be estimated from long-run proportions

C. is a tool that can be used to incorporate uncertainty into models

D. is the distribution of multiple random variables

Question 7 of 25 1.0 Points

The normal distribution is:

A. a discrete distribution

B. the single most important distribution in statistics

C. a binomial distribution with only one parameter

D. a density function of a discrete random variable

Question 8 of 25 1.0 Points

The mean of a probability distribution can be:

A. a positive number

B. a negative number

C. zero

D. all of the above

Question 9 of 25 1.0 Points

The standard normal distribution has a mean of ___ and standard deviation of ___, respectively.

A. 0 and 1

B. 1 and 1

C. 1 and 0

D. 0 and 0

Question 10 of 25 1.0 Points

The standard deviation of a probability distribution must be:

A. a negative number

B. a number between 0 and 1

C. less than the value of the mean

D. a nonnegative number

Question 11 of 25 1.0 Points

The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:

A. central tendency theorem

B. simple random sample theorem

C. central limit theorem

D. point estimate theorem

Question 12 of 25 1.0 Points

If Z is a standard normal random variable, the area between z = 0.0 and z =1.30 is 0.4032, while the area between z = 0.0 and z = 1.50 is 0.4332. What is the area between z = -1.30 and z = 1.50?

A. 0.0668

B. 0.0968

C. 0.0300

D. 0.8364

Question 13 of 25 1.0 Points

A statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.

77 81 74 77 79 73 80 85 86 73

83 84 81 73 75 91 76 77 95 76

90 85 92 84 81 64 75 90 78 78

82 78 86 86 82 70 76 78 72 93

Compute the standard deviation of these test scores. Place your answer, rounded to 2 decimal places in the blank. For example, 5.34 would be a legitimate entry.

Question 14 of 25 1.0 Points

Find the mean of the following probability distribution?

1 0.20

2 0.10

3 0.35

4 0.05

5 0.30

Place your answer, rounded to two decimal places, in the blank. When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 1.23 would be a legitimate entry.

Question 15 of 25 1.0 Points

In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.

Number of Products Purchased

Brands Purchased Fewer Same More Total

Same 10 14 24 48

Changed 262 82 8 352

Total 272 96 32 400

What is the probability that a consumer selected at random purchased fewer products than before? Place your answer, rounded to 4 decimal places, in the blank.

Question 16 of 25 1.0 Points

Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Number of Vehicles Involved

Did alcohol play a role? 1 2 3

Yes 60 110 30 200

No 40 215 45 300

100 325 75

What proportion of accidents involved alcohol and a single vehicle?

Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.

Question 17 of 25 1.0 Points

A daily lottery is conducted in which two winning numbers are selected out of 100 numbers. How many different combinations of winning numbers are possible? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.

Question 18 of 25 1.0 Points

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.

Question 19 of 25 1.0 Points

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

What is the probability of getting a score between 65 and 89 on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.

Question 20 of 25 1.0 Points

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend $20 or more at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.

Question 21 of 25 1.0 Points

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean 6.7 minutes and standard deviation 2.2 minutes. For a door selected at random, what is the probability the assembly line time will be between 5 and 10 minutes? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer.

Question 22 of 25 1.0 Points

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend less than $15 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.

Question 23 of 25 1.0 Points

Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.

What score represents the 60th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.

Question 24 of 25 1.0 Points

Using the standard normal curve, the Z- score representing the 10th percentile is 1.28. True

False

Question 25 of 25 1.0 Points

The left half under the normal curve is slightly smaller than the right half. True

False

**Additional Requirements**

Level of Detail: Only answer needed