Pre-test

Directions: Choose the letter of the best answer.

1. A distribution that illustrate the probability for each mean of all the samples with

identical sample size n is___________.

A. Frequency Distribution C. Sampling Distribution

B. Normal Distribution D. Non-probability

2. What is the population mean if the values are composed of 6, 9, and 12?

A. 7.0 B. 8.0 C. 9.0 D. 10.0

3. If the data set consists of 8, 9, 10, and 11, what is the sample mean?

A.9.0 B. 9.5 C. 10 D. 10.5

4. What is the population variance if the standard deviation of the given data set is 6?

A. 33 B. 34 C. 35 D. 36

5. What is the population standard deviation if the given population variance is 49?

A. 6.0 B. 6.5 C. 7.0 D. 7.5

6. What is the mean of the sampling distribution of its means if the given population

has a mean of 15.3?

A. 15.0 B. 15.3 C. 15.6 D. 15.9

7. What is the mean of the sampling distributions of its means when the given

population has a mean of 35?

A. 20 B. 25 C. 30 D. 35

8. What is the mean of the population if the mean of the sampling distribution of

means is 15.0?

A. 12.0 B. 13.0 C. 14.0 D. 15.0

9. Which of the following states that: "If samples of size n, where n is sufficiently large,

are drawn from any population with a mean and standard deviation , then the

sampling distribution of sample means approximates a normal distribution"?

A. Probability Distribution C. Central Limit Theorem

B. Normal Distribution D. Random Variable.

10. What is the variance of a sampling distribution of its means if it has a population

variance of 9.0 and n = 3?

A. 3.0 B. 3.1 C. 3.2 D. 3.3

Activity 2.1

The average number of milligrams (mg) of cholesterol in a cup of a certain brand

of milk tea is 500 mg, and the standard deviation is 30 mg. Assume that the data is

normally distributed.

A. If 30 cups of milk tea are randomly selected, what is the probability that the

cholesterol content will be less than 510 mg?

B. If 30 cups of milk tea are randomly selected, what is the probability that the

mean of the sample will be larger than 510 mg?

Activity 2.2

A LED company claims that the average life of the LED light bulbs it

manufactures is 1, 500 hours with a standard deviation of 500 hours. If a random

sample of 40 bulbs is chosen, what is the probability that the sample mean will be:

a. greater than 1, 400 hours?

b. less than 1, 400 hours?

CHECKING YOUR UNDERSTANDING

A prototype mountain bike tire has a design life of 12 800 km with a standard

deviation of 850 km. Fifty of such tires are manufactured and tested. On the

assumption that the actual population mean is 12 800 km and the actual population

standard deviation is 850 km, find the probability that the sample mean will be less

than 12 500 kilometers. Assume that the distribution of lifetime of such tires is normal.

POST TEST

Directions: Choose the letter of the best answer.

1. Which of the following statements is correct?

A. The mean of the sampling distribution of the means is greater than the

population mean.

B. The mean of the sampling distribution of the sample means is less than the

population mean.

C. The mean of the sampling distribution drawn from a population is always

equal to the population mean.

D. The means of the sampling distribution drawn from a population may be

equal, less than, or greater than the population mean.

2. What is the population mean if the population consists of values 3,6,9, and 12?

A. 5.5 C. 7.5

B. 6.5 D. 8.5

3. What is the sample mean if a sample consists of values 4,8,12, and 16?

A. 10 C. 12

B. 11 D. 13

4. What is the population variance if the population standard deviation of a data set

is 5?

A. 9 C. 16

B. 12 D. 25

5. What is the population standard deviation if the population variance of a set of data

is 36?

A. 6.0 C. 7.0

B. 6.5 D. 7.5

6. What is the mean of the sampling distribution of its means if the population has a

mean of 7.5?

A. 6.0 C. 7.0

B. 6.5 D. 7.5

7. What is the mean of the sampling distributions of its means if the population has a

mean of 20?

A. 10 C. 20

B. 15 D. 25

8. What is the mean of the population if the mean of the sampling distribution of the

means is 14.0?

A. 12.5 C. 13.5

B. 13.0 D. 14.0

9. If samples of size n, where n is adequately large, are randomly selected from any

of sample means approximates a normal distribution.

A. Probability Distribution C. Central Limit Theorem

B. Normal Distribution D. Random Variable

10. A battery manufacturer claims that its midgrade battery has an average life of 50

months with a standard deviation of 6 months. On the assumption that the

manufacturers' claim is true, find the probability that 30 randomly selected battery

of this type will last less than 48 months.

A. 0.0351 C. 0.0336

B. 0.0344 D. 0.0329