Question 1

How many different samples of size 3 can be collected from a population of ten items? ___________

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Question 2

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability that average student study time is between 18 and 22 hours?

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Question 3

Sampling from a population may be preferred because studying all the items in a population may be too ____________.

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Question 4

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. Given a class with 9 students, what is the probability that the class' average IQ score is between 85 and 115?

Accepted Answer

The sampling distribution of the sample mean for 9 students will have the same mean (100) but a standard deviation of 15/sqrt(9) = 5. The probability that the sample mean is between 85 and 115 can be found using the standard normal distribution, resulting in approximately 0.9974.

Question 5

What is the name of the standard deviation of the sampling distribution of the sample means called? ______________________

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Question 6

Sampling from a population may be preferred because, contacting or listing the entire population would be too ___________ consuming.

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Question 7

A __________________ assumes that each item or person in the population has an equal chance of being included.

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Question 8

If the size of a sample equals the size of the population, the sample error is ________.

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Question 9

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. You bought four tires. What is the probability that the average mileage of the four tires exceeds 66,000 miles?

Accepted Answer

The standard error of the mean for four tires is calculated as:
SE = σ/√n
where σ = 4000 (standard deviation), n = 4 (sample size)
SE = 4000/√4 = 2000

The z-score for a sample mean of 66,000 miles is:
z = (x̄ - μ)/SE = (66,000 - 60,000)/2000 = 3

Using a standard normal distribution table or calculator, the probability of getting a z-score of 3 or higher is very low: 0.0013. Therefore, the probability that the average mileage of the four tires exceeds 66,000 miles is 0.0013 or 0.13%. Thus, the best choice is A.

Question 10

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person would score 130 or more on the test?

Accepted Answer

The Z-score for a score of 130 is (130-100)/15 = 2. The probability of a Z-score being 2 or more is 0.0228, which corresponds to the probability of scoring 130 or more.

Question 11

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. For a set of four tires, what is the probability that the average tire life is between 57,000 and 63,000 miles?

Accepted Answer

To calculate the probability of the average tire life being between 57,000 and 63,000 miles, we need to use the formula for the standard error of the mean:

Standard Error = standard deviation / square root of sample size

Since we have four tires, the sample size is 4, so the standard error is:

Standard Error = 4000 / sqrt(4) = 2000

Next, we can calculate the z-score for each endpoint:

z1 = (57000 - 60000) / 2000 = -1.5
z2 = (63000 - 60000) / 2000 = 1.5

Using a standard normal distribution table or calculator, we can find the area between these two z-scores:

Area = 0.8664

Therefore, the probability that the average tire life is between 57,000 and 63,000 miles is 0.8664. The best choice is B.

Question 12

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup? _________

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Question 13

In the sampling distribution of the sample means, the standard error of the mean will vary according to the size of the sample. As the sample size n gets larger, the variability of the sampling distribution of the means gets ______________.

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Question 14

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. What is the probability that a tire will last 72,000 miles or more?

Accepted Answer

To find the probability that a tire will last 72,000 miles or more, we calculate the z-score: z = (72,000 - 60,000) / 4,000 = 3. Using the standard normal distribution table, the probability of a z-score being 3 or more is 0.0013.

Question 15

Auditors may select every 20^th file starting with say, the 5^th file in the top drawer. Then file numbers 25, 45, 65, 85, .... are audited. What type of sampling is this? _________________

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Question 16

Sometimes, sampling from a population may be preferred because collecting statistics may require that products be __________.

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Question 17

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person would score between 85 and 115?

Accepted Answer

To find the probability of a person scoring between 85 and 115, we need to calculate the area under the normal distribution curve between these two scores.

First, we find the z-scores for both values:

z-score for 85 = (85 - 100) / 15 = -1

z-score for 115 = (115 - 100) / 15 = 1

Using a z-table or calculator, we can find the area under the normal distribution curve between these two z-scores.

Area between z = -1 and z = 1 = 0.6826

Therefore, the probability that a person would score between 85 and 115 is 0.6826 or 68.26%.

Question 18

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. What is the probability that a tire lasts between 54,000 and 66,000 miles?

Accepted Answer

To find the probability that a tire lasts between 54,000 and 66,000 miles, we need to find the z-scores for each value and then use a z-table to find the area under the normal curve between those z-scores.

z-score for 54,000 miles: (54,000 - 60,000) / 4,000 = -1.5
z-score for 66,000 miles: (66,000 - 60,000) / 4,000 = 1.5

Using a standard normal distribution table or a calculator with built-in normal distribution functions, we can find the area under the curve between these two z-scores to be approximately 0.8664. This means that there is a 86.64% chance that a randomly selected tire will last between 54,000 and 66,000 miles. Therefore, the best choice is B (0.8664).

Question 19

If a population is normally distributed, then the sampling distribution of the sample means will be __________________________.

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Question 20

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. You enrolled in a class of 25 students. What is the probability that the class' average IQ exceeds 130?

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Quiz 8: Sampling Methods and the Central Limit Theorem