Topic: FINDING THE MEAN AND VARIANCE OF SAMPLING DISTRIBUTION OFNTHE SAMPLE MEANS

please answer letters:

A. (Multiple Choice Test)

B.

C.

A. Multiple Choice Test. Directions: Choose the letter of the correct answer. Write your answer on the space provided after the number. 1. The mean of the sampling distribution of the sample means is to the mean of the population. A. less than C. equal B. greater than D. both a and b 2. The variance of the population is given by the following formula: oz = E(x - H)2/ N , what does N represents? A. Sample size C. Variance B. Population size D. Mean 3. What are the steps in finding the mean of the sampling distribution of the sample means? a. multiply each sample mean by the corresponding probability, then add the results. b. multiply each sample mean by the corresponding probability C. subtract each sample mean to the population mean, then add the results. d. subtract each sample mean to the population mean 4. The Central Limit Theorem states that the mean of the sampling distribution of the sample mean is A. greater than the population mean. B. equal to the population mean. C. less than the population mean if the sample size is large. D. equal to the population mean divided by the square root of the sample size. 5. If a population has a mean of 7, what is the mean of the sampling distribution of the sample means? A. less than 7 B. larger than 7 C. closer to 7 D. exactly the same as 7 6. What happens to standard deviation and variance of the sampling distribution of the sample means as the sample size n increases? A. increases B. decreases ( stays the same D. none of these 7. Which of the following statements is NOT TRUE about Central Limit Theorem?A. The population mean and the mean of the sampling distribution of the means are exactly the same. B. The variance of the sampling distribution of the mean and the variance of population is equal. C. The Central Limit Theorem is used to approximate the distribution of the sample mean over the distribution of the population mean. D. If you take repeatedly independent random samples of size n from any population, then when n is large, the distribution of the sample mean will approach a normal distribution. 8.. It states that: "If random sample of size n are drawn from a population, then as n becomes larger, the sampling distribution of the mean approaches the normal distribution, regardless of the shape of the population distribution". A. Pythagorean Theorem B. Central Limit Theorem C. Probability Distribution D. Normal Distribution 9. Which of the following statements is correct?' a. The mean of the sampling distribution of the means is less than the population mean. b. The mean of the sampling distribution of the sample means is greater than the population mean. C. The means of the samples drawn from a population are always equal to the population mean. d. The means of the samples drawn from a population may be equal. Greater than or less than the population mean. 10. A certain population has a mean of 12.5 and a standard deviation of 4.7. If the random samples of size 7 is taken from this population, which of the following statements is correct? a. The mean of the sampling distribution of the sample means is equal to 12.5. b. The mean of the sampling distribution of the sample means is less than 12.5. c. The standard deviation of the sampling distribution of the sample means is 4.7 d. The standard deviation of the sampling distribution of the sample means is 15.1. 1 1. What is the shape of the sampling distribution of the means if random samples of size n become larger? left skewed b. right skewed c. normal d. rectangular For numbers 12 - 15, refer to the problem below. A population of 17-year old Senior High School students has a mean grade of 89 in Statistics and Probability with a standard deviation of 5. Assume that the variable is normally distributed. 12. If 20 randomly selected students are taken, what is the probability that their mean grade will be less than 87? a. 0.0267 b. 0.0367 c. 0.0467 d. 0.0567 13. If 50 students were randomly selected, what percentage that their mean grade will exceed 90? a. 7.93% b. 6.93% c. 5.93% d. 4.93% 14. What is the probability of the students to have an average grade between 88 and 91? a. 0.0793 b. 0. 1554 c. 0.0761 d. 0.2317 15. Which of following is the correct standard normal curve for number 12 question?3. b. Z = . 1.79 Z = -1.79 d. z = 1.79 z = 1.79 B. Directions: Perform what is being asked. Write your answer on the table provided below. Use another sheet of paper if it is necessary. (module 6) Given the population of numbers 3, 6, 8, 9, and 4. Suppose samples of size 8 are drawn from this population. 1. What is the mean and the variance of the population? 2. How many different samples of size 3 can be drawn from the population? List them with their corresponding mean. Samples Mean 3. Construct the sampling distribution of the sample means. Sampling Distribution of Sample Means Sample Mean (X) Frequency Probability [P(X)] 4. What is the mean of the sampling distribution of the sample means? Compare to the mean of the population. 5. What is the variance of the sampling distribution of the sample means? C.Direction: Perform by answering the worksheet provided with problem set to solve probability distribution of the sample means. A rubric is provided to score your accomplished task. (module s)Problem 1 The lengths of pregnancies are normally distributed with a mean of 260 days and a standard deviation of 12 days. If 30 women are randomly selected, find the probability that their lengths of pregnancy have a mean that is less than 255 days. Steps Solution 1. Identify the given information. 2. Identify what is being asked. 3. Identify the formula to be used. 4. Solve the problem 5. State your final answer. Problem 2. The weights of male students are normally distributed with a mean of 150 pounds and a standard deviation of 25 pounds. What is the probability that 25 randomly selected male students will have a mean weight of more than 155 pounds? Steps Solution 1. Identify the given information. 2. Identify what is being asked. 3. Identify the formula to be used. 4. Solve the problem. 5. State your final