Stat. & Proba. - Review on Sampling Distribution [Module 7]

Stat. & Proba. - Review on Central Limit Theorem [Module 7]

Let's Review

Central Limit Theorem

Open Ended

(Question 1)

If the population is consisting:

123 126 129 132 135

What is the population size?

Open Ended

(Question 2)

From the population 123 126 129 132 135

create 2 samples with a sample size of 3.

Multiple Choice

(Question 3)

From the population 123 126 129 132 135

How many possible samples can we create consisting of n=4?

• 2

• 3

• 4

• 5

Multiple Choice

(Question 4)

If the population can create 5 samples consisting of 4 observations (n=4), how many sample means can be made?

• 2

• 3

• 4

• 5

Multiple Choice

(Question 5)

Which of the following is a sampling distribution of the sample means?

A sampling distribution of the sample means shows every possible result a sample mean can take in every possible sample from a population and how often each result happens. 

Multiple Choice

(Question 6)

What is the shape of the of the sampling distribution of the means if the random samples of size n become larger?

• A. left skewed

• B. right skewed

• C. Normal

• D. rectangular

Multiple Choice

(Question 7)

What is the important assumption in the Central Limit Theorem that guarantees a normal sampling distribution?

• A. a sample that is large enough

• B. a large number of random samples

• a standard deviation equal to 1

• D. the population mean equal to 1

Multiple Choice

(Question 8)

Multiple samples with a size of 35 are taken from a known population, where μ=25 and σ=4 , as the sample size increases, what should be the value of the means approximate?

• A. 2

• B. 12.5

• C. 25

• D. 35

Multiple Choice

(Question 9)

What does  $\mu_{\overline{x}}=\mu$  mean?

• When you get the average of your sample means, it will equal to the population mean.

• As your sample size increases, the sampling distribution of the sample means approaches to normal distribution.

Multiple Choice

(Question 10)

Solve. A certain population has a mean of 20 and a standard deviation of 8. Sample size 16 are taken for the purpose of sampling distribution. What is the expected value of all these sample means?

• 18

• 19

• 20

• 21

 $\mu_{\overline{x}}=\mu$  

When you get the mean or average of the sample means, it will equal to the population mean.

Is the above illustration correct?

Multiple Choice

(Question 11)

Problem: "A parent enquires on cellphones for his senior high school student. He finds out that the average battery life of his preferred cellphone is 24 hours with a standard deviation of 7 hours. If the battery life of these cellphones approximates a normal distribution, and 5 cellphones are randomly selected, what is the probability that the average battery life is more than 20 hours?"

FROM THE ABOVE PROBLEM, DETERMINE THE POPULATION MEAN AND POPULATION STANDARD DEVIATION.

• 20 hours and 7 hours

• 5 hours and 7 hours

• 24 hours and 7 hours

• 24 hours and 20 hours

Multiple Choice

(Question 12)

Problem: "A parent enquires on cellphones for his senior high school student. He finds out that the average battery life of his preferred cellphone is 24 hours with a standard deviation of 7 hours. If the battery life of these cellphones approximates a normal distribution, and 5 cellphones are randomly selected, what is the probability that the average battery life is more than 20 hours?"

FROM THE ABOVE PROBLEM, DETERMINE THE STANDARD SCORE

• z = -1.02

• z = 1.28

• z = -1.02

• z = -1.28

Open Ended

(Question 13)

Problem: "A parent enquires on cellphones for his senior high school student. He finds out that the average battery life of his preferred cellphone is 24 hours with a standard deviation of 7 hours. If the battery life of these cellphones approximates a normal distribution, and 5 cellphones are randomly selected, what is the probability that the average battery life is more than 20 hours?"

What is asked in the problem? [Write in mathematical notation.]

Multiple Choice

(Question 14)

A certain population has a mean of 15.4 and a standard deviation of 5.6. If a random sample of 5 is taken from the population, which of the following statements is correct?

• The mean of the sampling distribution of the sample means is equal to 15.4.

• The mean of the sampling distribution of the sample means is less than 15.4.

• The standard deviation of the sampling distribution of the sample means is 5.6

• The standard deviation of the sampling distribution of the sample means is 15.4.