Answer the following questions and show your solutions.

1. Under the normal curve, the area to the right of the mean in A. 30% B. 47.72% C. 50% D. 68% 2. Which of the following parameters is the basis of the shape of the normal curve? A. mean B. standard deviation C. variance D. both A and B 3. Which of the following statements is the characteristic of a normal probability distribution? A. The three measures of central tendency such as mean, mode, and median are equal B. The three measures of central tendency such as mean, mode, and median are not equal C. The two measures of central tendency such as mean and mode are equal while the median is greater than zero D. The two measures of central tendency such as mean and mode are equal while the median is less than zero 4. Which of the following statements describe the concepts of empirical rule? A. It states that the data in the distribution lies within 100% B. It states that the data in the distribution lies within one (1), two (2), and three (3) of the standard deviation from the mean are approximately 68%, 95% and 99.70%, respectively C. It states that the data in the distribution lies within one (1). two (2), and three (3) of the standard deviation from the mean are exactly 68%, 95% and 99.70%, respectively D. It states that the data is asymmetric 5. Which of the following is an example of a discrete random variable? A. weight of newborn babies C. number of heads that will come out if you toss a coin twice B. body temperature of COVID-19 patients D. height of basketball players 6. Which of the following best describe the mean of a discrete random variable? A. It is the average value of a discrete random variable over numerous trials of an experiment. B. It is the lowest assumed value of a discrete random variable. C. It is the highest assumed value of a discrete random variable. D. It is the amount of spread, dispersion, or variability of the assumed value of a discrete random variable. 7. Which of the following best describe the variance and standard deviation of a probability? A. It is the lowest assumed value of a discrete random variable. B. It is the highest assumed value of a discrete random variable. C. It is the average value of a discrete random variable over numerous trials of an experiment. D. It is the amount of spread, dispersion, or variability of the assumed value of a discrete random variable. 8. Which of the following best describe the standard deviation of a probability distribution? A. It is twice the variance C. It is the product of the mean and the variance B. It is the square root of the variance D. It is the ratio of the mean and the variance 9. Given: x =125: u = 105: a = 16. Find the z score. A. - 1.25 B. - 1 C. 1 D. 1.25 10. Given: z = 2.25: u =70: o = 9. Find the value of x A. - 49.75 B. 35.11 C. 90.25 D. 148.5 11. The Enhance Community Quarantine of some places was lifted by our President Rodrigo Roa Duterte last May 15. 2020. Suppose that after the said ECO, one of the dieticians of well-known company conducted the survey about the effect of home quarantine on the health of the Filipino people. He found out that average weight for women is 70 kg with a standard deviation of 6 kg. If the weights are normally distributed, what is the z-score of a with a weight of 63? A. - 1.17 B. - 1.16 C. 1.16 D. 1. 1712. Referring to number 11, what is the z-score of a woman with a weight of 85kg? A. - 2.50 B. - 1.50 C. 1.50 D. 2.50 13. The ages of Senior High students enrolled at Sta. Catalina National High School are normally distributed with a mean of 17 years and a standard deviation of 2.5 years. If a student is selected at random, what is the probability that his age is under 16 years? A. 15.54% B. 34.46% C. 68.92% D. 84.56% 14. The weekly sales of ABM students on their "Go Business" project are normally distributed with a mean of P4,250 and a standard deviation of P300. How many percent of their weekly sales are over P4,700? A. 6.68% B. 13.36% C. 86.63% D. 93.32% 15. In problem number 14, how many percent of the ABM students' weekly sales are less than P4,700? A. 6.68% B. 13.36% C. 86.63% D. 93.32% For numbers 16 - 18, refer to the table below. 2 6 8 P(X) 0.12 0.29 0.24 0.35 16. Which of the following is the correct formula to find the expected value of the probability distribution? A. E(X) = [[X . P(X)] B. E(X) = =[X2 . P(X)] C. E(X) = =[X2 . P(X)] - p2 D. E(X) = =[X2 . P(X)] - Hz 17. What is the mean of the given probability distribution? A. 4.85 B. 5.64 C. 6.32 D. 7.12 18. Which of the following is the appropriate value for the variance? A. 4.35 B. 4.36 C. 4.37 D. 4.38 19. Find the z value of the graph that corresponds to the given area. A. - 2.10 B. - 2.07 C. - 2.03 0.0228 D. - 2.00 20. Find the z-value of the graph that corresponds to the given area. A. - 2.24 B. - 2.25 C. 2.24 D. 2.25 0.0125