STATISTICS AND PROBABILITY

Quarter 3-Week 7 & 8

Module 3: SAMPLING AND SAMPLING DISTRIBUTION SAMPLING DISTRIBUTION OF THE SAMPLE MEAN USING CENTRAL LIMIT THEOREM

LESSON 2: PROBLEMS INVOLVING SAMPLING DISTRIBUTION OF THE SAMPLE MEAN

What is It

Activity 1. Fix the Problem!

Directions: Read and analyze the given problems below. Write the solutions and final answer on a separate sheet of paper.

1. ILAW Manufacturing company produces bulbs that last a mean of 900 hours with a standard deviation of 110 hours. What is the probability that the mean lifetime of a random sample of 15 of these bulbs is less than 850 hours?

2. A school principal claims that grade 11 students have a mean grade of 86 with a standard deviation of 4. Suppose that the distribution is approximately normal. What is the probability that a randomly selected grade will be greater than 82 but less than 90?

population multiplied by the sample size n. D. The standard deviation of the sampling distribution of the means is equal to the standard deviation of the population multiplied by the square root of the sample size n. 2. Which of the following refers to the standard deviation of a sampling distribution? A. It is the sum of squares. B. It is the standard error of the mean. C. It only applies only to population data. D. It can be larger than the standard deviation for the population. 3. Who is the French-born Mathematician who proved the first version of the Central Limit Theorem? A. Abraham de Moivre B. Aristotle C. Aleksander Lyapunov D. Rene Descartes 4. Which of the following properties describes the sampling distribution of the sample mean? A. The mean of the sampling distribution of the means is equal to the mean of the population. B. As the sample size n decreases, the sampling distribution of the means approaches a normal distribution. C. The variance of the sampling distribution of the means is equal to the variance of the population multiplied by the sample size n. D. The standard deviation of the sampling distribution of the means is equal to the standard deviation of the population multiplied by the square root of the sample size n. For numbers 5-7, use the problem below. The average time it takes for high school students to complete certain examination is 46.2 minutes. The standard deviation is 8 minutes. There will be 50 random samples to be selected. Assume that the variable is normally distributed. 5. What is the population mean in the given problem? A. O B. 8 C. 46.2 D. 50 6. What is the value of n in the given problem? AO B. 8 C. 46.2 D. 50 7. If 50 random selected high school students take the exam, what is the probability that the mean time it takes the group to complete the test will be less than 43 minutes? A. 0.23% B. 2.3% C. 3% D. 23% 8. What is the mean of sampling distribution if mean of population is 25? A. 25 B. 5 C. 30 D. 35 9. What is the standard deviation of sampling distribution if standard deviation of population is 35 and sample size is 9? A. 11.67 B. 12.67 C. 13.67 D. 14.67 10. If a population has a mean of 6.5, what is the mean of the sampling distribution of its means? A. 5.6 B. 6.5 C. 6.7 D. 65 Statistics and Probability Q3_W7&8| 9What is It Activity 1. Fix the Problem! Directions: Read and analyze the given problems below. Write your solutions and final answer on a Separate sheet of paper. 1. ILAW Manufacturing company produces bulbs that last a mean of 900 hours with a standard deviation of 110 hours. What is the probability that the mean lifetime of a random sample of 15 of these bulbs is less than 850 hours? 2. A school principal claims that grade 11 students have a mean grade of 86 with a standard deviation of 4. Suppose that the distribution is approximately normal. What is the probability that a randomly selected grade will be greater than 82 but less than 90?What's More Directions: Read carefully each item. Use a separate sheet for your answers. Write only the letter of the best answer for each test item. 1. Which of the following is correct about the sampling distribution of the sample mean using the Central Limit Theorem? A. The mean of the sampling distribution of the means is not equal to the mean of the population. B. As the sample size n increases, the sampling distribution of the means approaches a normal distribution. C. The variance of the sampling distribution of the means is equal to the variance of the Statistics and Probability Q3_W7&8