Help me answer all of the following activities and please do follow the page numberings thank you in advance

Activity 3. Direction: Read and analyze the situation below. Answer the questions as required. 1. According to the article - Social Media Usage in the Philippines by Sanchez (2020), the Philippines has one of the highest numbers of social network users across Southeast Asian nations with approximately 67% social media penetration rate. On average, Filipinos spent almost four hours using social media where Facebook was the most used platform. Assume you know the probability distribution of the number of hours an individual spends on Facebook per week in a certain municipality of Pangasinan. The data are presented below. Number of hours 2 3 4 5 6 using Facebook (X) Probability P(X) 0.13 0.21 0.32 0.21 0.13 a. Compute for the mean, variance, and standard deviation. b. What is the probability that an individual spends at least 4 hours using Facebook weekly? 83. The Pangasinan Provincial Board approved an ordinance of mandatory wearing of faceshield in the province during this public health crisis due to coronavirus disease. What is the mean and standard deviation of the distribution if you know that those who violated the ordinance are being charged with different amounts with the following probabilities? Fine (in pesos) 1,000 2,500 5,000 Probability 0.25 0.45 0.30 A) mean of 2875; standard deviation of 1515.54 B) mean of 2857; standard deviation of 1515.54 C) mean of 2875; standard deviation of 1515.45 D) mean of 2857; standard deviation of 1515.45 4. In a specific municipality, a non-profit group organizes a raffle for a good cause. One thousand raffle tickets cost P1.00 each. Assume that everyone has an equal chance of winning the P300, P200, and P100 prizes, and that an individual has an estimated winning of 0.25. What can you conclude? A) On average, an individual will lose 0.25 for every ticket purchased. B) On average, an individual will gain 0.25 for every ticket purchased. C) On average, an individual will win the raffle with any prizes. D) On average, an individual will not win the raffle with any prizes. 5. Suppose a discrete random variable X has the following probability distribution: X 23 34 45 56 P(X) 0.33 0.24 n 0.12 What is the value of n? A) 0.13 B) 0.21 C) 0.31 D) 0.41 6. Suppose there are 7 outcomes to an experiment in a discrete random variable. You have computed the corresponding probability of the outcomes: 0.30, 0.30, 0.40, 0.20, 0.25, -0.25, -0.20. What can be said about the probability of the outcomes? A) One of the outcomes will have effect 40% of the time. B) Two of the probabilities or outcomes will never take place. C) The sum of all the probabilities is 1. D) The probabilities of the outcomes range from 0 and 1. 7. Which of the following measures defines the mathematical expectation of a probability distribution? A) mean B) standard deviation C) sum D) variance 18X 50,000 700,000 B) D) X 49,980 700,020 0.998 0.002 P(X) 0.998 0.002 P(X) 14. Given that a 35-39 woman will have a 0.0002 chance of not surviving within a year, what is the probability that she will survive within a year? A) 0.998 B) 0.9998 C) 0.99998 D) 0.999998 15. What is the expected value of Hermari Life Insurance's profit on the policy? A) 49,805 B) 49,085 C) 49,850 D) 49,980 ACTIVITY 14 Solve the following problems as required. 1. Based on data from the 2019 Philippine Statistics Authority Death Statistics Table, the probability that a 70-74 year old man will not be alive in 1 year is 0.1028. Assume Sipnayan Life Insurance, an insurance provider, charges P40,000 to cover a 70-74 year old man for the whole year. If he does not live within a year, the insurance firm will pay P380,000 to his survivor as a death benefit. Determine and interpret the mathematical expectation of profit on the policy of the insurance company. 2. Maria Ophelia Louise intends to invest P500,000 in establishing a company FAROAH clothing line. She estimates that she has a 0.20 probability of making a P500,000 profit, a 0.25 probability of making a P2,500,000 profit, a 0.35 probability of making no profit. What is the expected value of the profit? Should Maria Ophelia Louise continue on this kind of investment with her clothing line? 20A) 3.05 B) 3.50 C) 5.03 D) 5.30 11. What value corresponds to the variance of the distribution? A) 1.17 B) 1.71 C) 2.17 D) 2.71 12. What is the probability that Hananiah Hermarie used at least 5 yellow pads? A) 0.30 B) 0.50 C) 0.70 D) 0.75 13. Which of the following corresponds to the standard deviation of the distribution? A) 1.31 B) 1.33 C) 1.35 D) 1.37 14. Which of the following refers to the sum of the product of X and P(X) of a discrete random variable? A) variance B) probability C) expected value D) deviation 15. Which of the following is a TRUE statement? A) The probability distribution of a discrete random variable can be negative. B) The expected value of a probability distribution is always equal to 1. C) The variance is equal to the standard deviation of a probability distribution. D) The mathematical expectation is the same with the mean value of a probability distribution of a discrete random variable. ACTIVITY 7 1. Suppose John Paul Gabriel, a Grade 11 TVL HE learner, recorded the number of cookies baked per day as part of his subject Bread and Pastry Production. The data are as follows: X (no. of cookies) 15 20 25 30 35 40 P(X) 0.10 0.15 0.25 0.25 0.15 0.10 a. What is the probability that John Paul Gabriel will bake more than 25 cookies? b. What is the probability that John Paul Gabriel will bake less than 30 cookies? c. Find the mathematical expectation (mean) and variance of the given discrete random variable. 2. The Grade 11 HUMSS learners wanted to know the number of ballpens used by Grade 11 learners in answering their modules in different subjects for the First Semester of the School Year 2020-2021. The following distribution was documented: X (no. of ballpens) 4 5 6 7 8 9 12Direction: Read and understand each item, then choose the letter of the best answer and write it on a separate sheet of paper. 1. Which of the following are TRUE statements? I. The standard deviation of a random variable is equal to zero if it takes a single value.P(X] 0.05 0.13 0.17 0.28 0.22 0.15 a. What is the probability that a Grade 11 learner will use less than 7 ballpens in answering modules? b. What is the probability that a Grade 11 learner will use more than 6 ballpens in answering modules? c. Compute for the mean, variance, and standard deviation of the given discrete random variable. 13A) 1.0 B) 1.5 C) 2.0 D) 2.5 7. What is the variance of the probability distribution? A) 1.03 B) 1.05 C) 1.30 D) 1.50 2 8. What is the standard deviation of the probability distribution? A) 1.01 B) 1.02 C) 1.14 D) 1.22 9. What is the probability that more than 2 male individuals will be in any household? A) 0.35 B) 0.65 C) 0.90 D) 1.00 10. Suppose you are one of the 1,000,000 people who send their names through text in an online raffle promo with 1 top prize of P50,000, 10 prizes of P20,000 and 100 prizes of P10,000. What will be your expected winnings? A) 0.80 B) 1.00 C) 1.25 D) 1.50 11. Your mother wants you to choose one of the three boxes and pick a bill after. The first box has two P1000-bill and eighteen P200-bill. On the other hand, the second box contains ten P1000-bill and forty P100-bill and the third box has 14 P20-bill. Which of the following claims is TRUE with regards to the expected winnings? A) The first box has the highest expected winning. B) The expected winning of the second box is lower than of the third box. C) The expected winning of the third box is higher than of the first box. D) All boxes have the same expected winnings. 12. The Pangasinan Provincial Board approved an ordinance of mandatory wearing of face shield in the province during the public health crisis due to coronavirus disease. Suppose you have known that those who violated the ordinance are being fined with various amounts with the following probabilities, what would be the mean and the standard deviation of the distribution? Fine (in pesos) 1,000 2,500 5,000 Probability 0.45 0.35 0.20 A) mean of 2326; standard deviation of 1493.55 B) mean of 2325; standard deviation of 1493.95 C) mean of 2324; standard deviation of 1493.35 D) mean of 2323; standard deviation of 1493.75 3ACTIVITY 5 1. Assume that Raymund Gregory, a Grade 11 student, is scheduled to take a 20-item summative assessment in Physical Science, Statistics and Probability, and Research in Daily Life I. He knows he has a 50% chance of having a perfect score based on his previous summative evaluations in each subject. Given that X represents the number of perfect scores Raymund Gregory will obtain, determine the values and corresponding probabilities of the distribution of X. 2. Consider drawing a card from a shuffled fair of playing cards. In a game created by Yuno and Asta, the highest number in each case determines the winner. Asta makes two cards, one with the number 9 and the other with the number 19, and then draws one card. Yuno, on the other hand, shuffles and draws one card from the six cards he made, four of which have tens and two of which have twenty. a. In the given situation, which character would you prefer - Yuno or Asta? Give a reason for your decision. b. To make the game equal, if Yuno receives P 50.00 for each win, what should Asta receive for each win? ACTIVITY 6 Read and understand each item, then choose the letter of your answer and write it on your answer sheet. 1. If F(X) = _*, what are the possible values of X for it to be a probability 150 distribution? A) 10, 30, 50 C) 50, 60, 70 B) 30, 50, 70 D) 60, 70, 80 2. For x = 10, 20, and 30, can the function h(x) = _+ be the probability 75 distribution for some random variable? A) Yes. B) No, since none of the probabilities can be negative. 100.35 0.30 0.25 0.20 0.15 0.10 0.05 32 34 36 38 40 Number of Learners Present in a Week (X) 1. Find the probability that in a given week: a. at most 36 learners are present during an online class in Statistics? b. at least 36 learners are present during an online class in Statistics? c. at least 34 learner are present during an online class in Statistics? d. exactly 40 learners are present during an online class in Statistics? 2. What is the average number of learners present during an online class in a week? 3. Determine the variance and standard deviation of the given random variable. ACTIVITY 1 Read and analyze the situation given below. Mr. Tamondong, a PE teacher, manages to give an assessment composed of 4 performance tasks in the 3nd Quarter of the school year. He noticed that some learners did not submit some of the performance tasks. He used to check the probability distribution of the submitted performance tasks and the data is presented below. 6GINTO Investment gives your parents a PILAK Investment TANSO Investment 25% chance of gives your parents a gives your parents 50% chance of an 85% chance of making making P250,000.00, P100,000.00, P500,000.00, otherwise they lose otherwise they make otherwise they lose P175,000.00 only P5,000.00 P50,000.00 Questions: 1. What sort of investment should your parents make? Give a justification for your choice. 2. If your parents assume they will go bankrupt if they do not make a profit, which investment should they make for the best chance of avoiding bankruptcy? Give a reason for your answer. 152. A miiktea shop owner detemn'nes the number of milktea that is consumed each day. {a} Find the mean. variance, and standard deviation for the distribution shown below. {b} If the owner stated that 150 cups of mktea were consumed in one day. do you think that this is a credible assertion? Probability Put] 0 4o 3. The number of people using Shopee-lazada app per day in San Carlos City is found in the distribution below. Number of Shopee-Lasada app 100 150 2m 250 see users {X} Probability Pm D. 15 0.20 (1.30 D. 15 0.20 a. Compute for the mean. variance. and standard deviation for the given probability distribution h. 1What is the probability that fewer than 2130 or more than 250 people use Shopce-Iazada app on a given day? ACTIVITY 4 complete each statement below. The expected value of a discrete random variable is The variance is while the standard deviation is To nd for the meat:1 Meanwhile, to compute for the variance, In addition, to detecmine the standard deviation, - 0.45 0.40 0.35 2 0.30 0.25 Probability Distribution (Submission) 0.20 20.15 0.10 9 0.05 0.00 0 Number of Performance Tasks Submitted (PE) Based on the data offered, answer the following questions: 1. What is the sum of all the probabilities of the given random variable (i.e. submission of performance tasks by the learners)? 2. What have you noticed about the probability distribution? Can it take a negative value? State your reason. 3. What is the average number of performance tasks submitted to Mr. Tamondong? 4. Compute for the values of the variance as well as with the standard deviation of the probability distribution? 7C) No, since none of the probabilities can be greater than 1. D) No, since the sum of the probabilities is not equal to 1. For items 3-5, consider the following discrete probability distribution: X 0 1 2 3 4 P(X) 3/15 3/15 3/15 3/15 3/15 3. What is the expected value of the probability distribution? A) 1 B) 2 C) 3 D) 4 4. What is the variance of the probability distribution? A) 1 B) 2 C) 3 D) 4 5. What is the standard deviation of the probability distribution? A) 1.40 B) 1.41 C) 1.42 D) 1.43 For items 6-8, refer to the scenario and table provided below. The number of female individuals living in the household on a randomly selected barangay is described by the following probability distribution. X 0 1 2 3 4 P(X) 0.10 0.20 0.40 0.20 0.10 6. What is the mean of the probability distribution? A) 1.0 B) 1.5 C) 2.0 D) 2.5 7. What is the variance of the probability distribution? A) 1.10 B) 1.15 C) 1.20 D) 1.25 8. What is the standard deviation of the probability distribution? A) 1.10 B) 1.20 C) 1.30 D) 1.40 9. If the variance of a random probability distribution is 1.05, what is the standard deviation? A) 1.0125 B) 1. 1025 C) 1.125 D) 1.25 For questions 10-13, refer to the following. Suppose Hananiah Hermarie, a Grade 11 learner, recorded the probability distribution for the number of yellow pads that she used in answering his modules in different subjects. X 3 4 5 6 7 P(X) 0.10 0.20 0.25 0.20 0.25 10. What is the mathematical expectation of the given probability distribution? 11II. The standard deviation of a random variable can never be negative. III. As the number of observations increases, the mean of a random variable will get closer and closer to a particular value. A) I and II C) II and III B) I and III D) I, II and III 2. Given that x = 1, 2, and 3. Is it possible for the function g(x) = _+5 to be the 21 probability distribution for some random variable? A) Yes. B) No, since none of the probabilities can be negative. C) No, since none of the probabilities can be greater than 1. D) No, since the sum of the probabilities is not equal to 1. 3. If P(X) = *_ what are the possible values of X for it to be a probability distribution? A) 0, 2, 3 C) 2, 3, 4 B) 1, 2, 3 D) 3, 4, 5 For items 4-5, consider the following discrete probability distribution: X O 2 3 4 P(X) 1/5 1/5 1/5 1/5 1/5 4. What is the expected value of the probability distribution? A) 1 B) 2 C) 3 D) 4 5. What is the variance of the probability distribution? A) 1 B) 2 C) 3 D) 4 For items 6-9, refer to the scenario and table provided below. The number of male individuals living in the household on a rand barangay is described by the following probability distribution. imly selected X 0 1 2 3 4 P(X) 0.10 0.25 0.30 0.25 0.10 6. What is the mean of the probability distribution? 28. A research team gathered the following discrete probability distribution. In this distribution X represents the number of mobile phones owned by a family residing in Merryland Subdivision. What is the mean value of the distribution? X 0 1 2 3 P(X) 0.10 0.10 0.50 0.30 A) 1.0 B) 1.5 C) 2.0 D) 2.5 For questions 9-12, refer to the following. Suppose a certain rural bank in your municipality offered you an investment opportunity. Its outcomes and probabilities are presented in the following table. X - P 5,000.00 PO P 5,000.00 P(X) 0.30 0.40 0.30 9. Which of the following statements is true? A) The distribution is symmetric. C) The distribution is bimodal. B) The distribution has a negative mean. D) The distribution has a mean of 3. 10. What is the mean of the distribution? A) P 5,000.00 B) P 2,500.00 C) P 1,000.00 D) P 0.00 11. What is the variance of the distribution? A) P150,000,000 B) P15,000,000 C) P1,500,000 D) P10,500,000 12. What is the standard deviation of the distribution? A) P 3872.98 B) P 3827.98 C) P 3872.89 D) P 3827.89 For questions 13-15, refer to the following. Assume that an insurance firm, Hermari Life Insurance, provides a one-year term life insurance policy to a 35-39 year old woman. The woman pays a premium of P50,000. If she dies within a year, the insurance firm will give her beneficiaries P750,000. According to the 2019 Philippine Statistics Authority Death Statistics Table, the probability that a 35-39 year old woman will not survive in 1 year is 0.0002. 13. Given X as the net gain of Hermari Life Insurance, which of the following tables of values represents the probability distribution of X? X 50,000 700,000 A) C) X 49,980 700,020 P(X) 0.9998 0.0002 0.9998 0.0002 P(X) 19In a certain school, the number of learners present during an online class in Statistics per week is a random variable represented by X. The probability distribution for X is presented below. 5ACTIVITY 10 Direction: Read and analyze the situations. Answer the questions as required. 1. Suppose Mahika Kagamitan Center will hold its annual raffle bonanza. A flat screen TV worth P17,500 is up for grabs with 5,000 tickets priced at P50.00 each. What is the expected value of Juan Emilio's gain if he buys 15 tickets? 2. Assume there are 100 prizes of P100, 50 prizes of P200, and five prizes of P1000 in a lottery. What is a fair price to charge for a ticket if there are 5.000 tickets to be distributed and sold? 3. Assume there are three prizes available in an online raffle for a good cause: one P5,000 prize, one P3,000 prize, and one P1,500 prize. A total of 1,000 tickets will be sold for P20 each. What is the mathematical expectation if a person buys one ticket? ACTIVITY 11 Complete the statement below. 1. The is the mean of a random variable. 2. If expected value is positive, then a is expected 3. If expected value is negative, then a is likely to occur. 4. To compute for the expected value, the formula to be used is 5. In obtaining the mathematical expectation of a certain random variable, get the sum of all the products formed by the and 1613. A non-profit organization in a certain municipality organizes a raffle for a cause. One thousand raffle tickets are sold for P1.00 each. Suppose each has an equal chance of winning for the following prizes: P300, P200, P100 and an individual has an expected winning of -0.30. What can you conclude? A) On average, an individual will lose 0.30 per ticket purchased. B) On average, an individual will gain 0.30 per ticket purchased. C) On average, an individual will win the raffle with any prizes. D) On average, an individual will not win the raffle with any prizes. 3 14. Suppose a discrete random variable X has the following probability distribution: X 23 34 45 56 P(X) 0.35 0.23 n 0.11 What is the value of n? A) 0.13 B) 0.21 C) 0.31 D) 0.41 15. Suppose there are 7 outcomes to an experiment in a discrete random variable. You have computed the corresponding probability of the outcomes: 0.40, 0.40, 0.20, 0.10, 0.35, -0.35, -0.10. What can be concluded about the probability of the outcomes? A) One of the outcomes will have effect 40% of the time. B) Two of the probabilities or outcomes will never take place. C) The sum of all the probabilities is 1. D) The probabilities of the outcomes range from 0 and 1.ACTIVITY 12 Suppose you will be designing a game or problem using expected value. By filling out the table below, you will construct a problem where the expected value represents a gain or win and/ or illustrates a drawback eventually. The first item has already been presented for your reference. Gain Loss Lottery Assume you will choose a number Assume you'll choose a number from from 1 to 100 and pay P5.00. If|1 to 100 and pay P15.00. You will be your number is called, you will be given P1000 if your number is called awarded P1000. You have 0.01 You have a 0.01 chance of winning chance to win. Determine the Calculate your profit's expected expected value of your profit. value. Raffle Draw Insurance/ Investment ACTIVITY 13 Choose the letter of your answer and write it on your answer sheet. 1. Suppose you are one of the 10,000 people who send in their name through text in an online raffle promo with 10 prizes of P5,000, 25 prizes of P2,000 and 50 prizes of P1,000. What will be your expected winning? A) 5 B) 10 C) 15 D) 20 2. Your mother wants you to choose one of the three boxes and pick a bill after. The first box has two P1000-bill and eighteen P200-bill. On the other hand, the second box contains ten P1000-bill and forty P100-bill and the third box has 14 P20-bill. Which of the following claims is true with regards to the expected winning? A) The first box has the highest expected winning. B) The expected winning of the second box is lower than of the third box. C) The expected winning of the third box is higher than of the first box. D) All boxes have the same winnings. 17ACTIVITY 8 The mother of Raymund Gregory wants him to choose one of the three boxes and pick a bill after. The three boxes containing different denominations are shown below. Makisig Box Mayumi Box Maharlika Box 17 pcs. 16 pcs 15 pcs 8 e O 1000 100 200 3 pcs. 4 pcs 5 pcs Images source: https:// en. wikipedia.org/ wiki/ Banknotes_of_the_Philippine peso Questions: 1. What is the expected winnings for each box? 2. Which box would you recommend to Raymund Gregory if you were his friend? Give a reason for your decision. ACTIVITY 9 Suppose your parents wanted to invest their money in a certain financial institution. The three financial institutions have the following offers: 14