2141:58 Elllocal_media1163563...Let's review. Solve for x in terms of another variable.1. ах %3Db2. х + у%3D13. y = mx + b4 a+b = 15. z =Answers:y-b1.X = b/a2. x = 1-y3. х-4. x = a +b 5. x = zo + uтFill Me UpComplete the table below by filling in the correct value of the required variable. Usethis formula zX-H and solve.X23184-1.17?12530?5154751000.565?15.55.5This time, you need to reflect on the following questions. Answer the following questions:1. How did you find the activity?2. How were you able to find the value of z'3. Can you derive the formula in finding the value of x?4. Do you think it is possible to solve for the u and o given the value of x and z?The activity allows you to manipulate the given data and the missing value throughderivation. In this case, you convert the raw score (x) into the standard score (z) using theformula z = . You substitute the given values and uses properties of equality and algebraicrules to obtain the needed data.In solving real-life problems involving the normal curve, it is particularly important toconvert a random variable x to a standard normal variable or z-score. This procedure is knownas "standardizing" or "standardization" of a random variable, where a standardized value iscalled a z-score. A z-score is a measure of the number of standard deviations (o) a particulardata value is away from the mean (u).EXAMPLE:Suppose your score on a test in Probability and Statistics is 39 and the scores arenormally distributed with a mean of 33 and standard deviation of 3, then your score is exactly2 standard deviations above the mean. If you scored 30, then it is exactly 1 standard deviationbelow the mean. All values that are above the mean have positive z-scores and all values thatare below the mean have negative z-scores. If you obtained a z-score of -3, this means that yourscore is 3 standard deviations below the mean, that is, 33 – 3(3) = 33 – 9 = 24.Given any value x from a normal distribution with mean u and standard deviation o, toconvert x to a z-score (standard normal score), you need to;(a) Subtract the mean u from x.(b) Divide this quantity, x – µ, by the standard deviation o. 3671:59 Elocal_media1163563..Note: In this example, we do not have ol and o2, and µl and µ2 since we are describing asingle population. Thus, ơ1 = o2 = o and µl = µ2 = µ. Furthermore, we need to review ouralgebra specifically on systems of linear equation. So,40 = -20 + µequation 1equation 270 = lo + µSubtract equation 1 from equation 2, we have40 = -20 + H70 = lo + µ30 = lo - (-20)30 = 30equation 1equation 2the difference10 = 0simplifyThe standard deviation of the population is 10. To obtain the mean, substitute it toeither equation 1 or 2.40 = -20 + µ70 = lo + µBoth agrees that the mean of the population is 60.= 40 = -2(10) + u= 70 = 1(10) + µ= 60 = µ= 60 = µTherefore,1. It is possible to determine the population's mean and standard deviationgiven only the raw score (x) and its corresponding standard score (z).2. The mean and standard deviation of the population is 60 and 10,respectively.Independent ActivitySupply the needed information by solving the missing value.H= 40,µ= 218,µ= 30,u= 105,H= 145,1. х %3D25,2. z = -2.25,3. х %3D 39,4. x = 125,5. z = 1.11,o = 6,o = 36,o = 3,o = 8,o = 20,z =?x =?z =?z =?x =?LESSON 5.Computing Probabilities and Percentile Using the Standard Normal TableHave you tried comparing your previous performance to your present performance? Orcomparing your performance in different subjects like Math and 158 English? Which of thetwo subjects are you better - Math with a score of 30 whose mean is 25 and a standard deviationof 5 or English with a score of 32 whose mean is 27 and a standard deviation of 6? These aresimple questions we thought do not require statistics, but it is. In this lesson, this module willguide you on how to compute probabilities and percentile using the z - table.Let's review.1. Convert 0.4783 into percent.2. What is the equivalent of 38.45% in decimal?3. What is the product of 450 and 0.2356?(Round off your answer into nearest whole number)4. What is the 25% of 100?5. What is the total area of a normal curve?

Question

2141:58 Elllocal_media1163563...Let's review. Solve for x in terms of another variable.1. ах %3Db2. х + у%3D13. y = mx + b4 a+b = 15. z =Answers:y-b1.X = b/a2. x = 1-y3. х-4. x = a +b 5. x = zo + uтFill Me UpComplete the table below by filling in the correct value of the required variable. Usethis formula zX-H and solve.X23184-1.17?12530?5154751000.565?15.55.5This time, you need to reflect on the following questions. Answer the following questions:1. How did you find the activity?2. How were you able to find the value of z'3. Can you derive the formula in finding the value of x?4. Do you think it is possible to solve for the u and o given the value of x and z?The activity allows you to manipulate the given data and the missing value throughderivation. In this case, you convert the raw score (x) into the standard score (z) using theformula z = . You substitute the given values and uses properties of equality and algebraicrules to obtain the needed data.In solving real-life problems involving the normal curve, it is particularly important toconvert a random variable x to a standard normal variable or z-score. This procedure is knownas &#34;standardizing&#34; or &#34;standardization&#34; of a random variable, where a standardized value iscalled a z-score. A z-score is a measure of the number of standard deviations (o) a particulardata value is away from the mean (u).EXAMPLE:Suppose your score on a test in Probability and Statistics is 39 and the scores arenormally distributed with a mean of 33 and standard deviation of 3, then your score is exactly2 standard deviations above the mean. If you scored 30, then it is exactly 1 standard deviationbelow the mean. All values that are above the mean have positive z-scores and all values thatare below the mean have negative z-scores. If you obtained a z-score of -3, this means that yourscore is 3 standard deviations below the mean, that is, 33 – 3(3) = 33 – 9 = 24.Given any value x from a normal distribution with mean u and standard deviation o, toconvert x to a z-score (standard normal score), you need to;(a) Subtract the mean u from x.(b) Divide this quantity, x – µ, by the standard deviation o. 3671:59 Elocal_media1163563..Note: In this example, we do not have ol and o2, and µl and µ2 since we are describing asingle population. Thus, ơ1 = o2 = o and µl = µ2 = µ. Furthermore, we need to review ouralgebra specifically on systems of linear equation. So,40 = -20 + µequation 1equation 270 = lo + µSubtract equation 1 from equation 2, we have40 = -20 + H70 = lo + µ30 = lo - (-20)30 = 30equation 1equation 2the difference10 = 0simplifyThe standard deviation of the population is 10. To obtain the mean, substitute it toeither equation 1 or 2.40 = -20 + µ70 = lo + µBoth agrees that the mean of the population is 60.= 40 = -2(10) + u= 70 = 1(10) + µ= 60 = µ= 60 = µTherefore,1. It is possible to determine the population's mean and standard deviationgiven only the raw score (x) and its corresponding standard score (z).2. The mean and standard deviation of the population is 60 and 10,respectively.Independent ActivitySupply the needed information by solving the missing value.H= 40,µ= 218,µ= 30,u= 105,H= 145,1. х %3D25,2. z = -2.25,3. х %3D 39,4. x = 125,5. z = 1.11,o = 6,o = 36,o = 3,o = 8,o = 20,z =?x =?z =?z =?x =?LESSON 5.Computing Probabilities and Percentile Using the Standard Normal TableHave you tried comparing your previous performance to your present performance? Orcomparing your performance in different subjects like Math and 158 English? Which of thetwo subjects are you better - Math with a score of 30 whose mean is 25 and a standard deviationof 5 or English with a score of 32 whose mean is 27 and a standard deviation of 6? These aresimple questions we thought do not require statistics, but it is. In this lesson, this module willguide you on how to compute probabilities and percentile using the z - table.Let's review.1. Convert 0.4783 into percent.2. What is the equivalent of 38.45% in decimal?3. What is the product of 450 and 0.2356?(Round off your answer into nearest whole number)4. What is the 25% of 100?5. What is the total area of a normal curve?

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Let's review. Solve for x in terms of another variable. 1. ах %3Db 2.х + у%31 3. у %3D mx + b 4. a+b = 1 X-u 5. z = Answers: 1. х%3Dba 2. х3 1-у 3. х%3D 4. х%3а+b 5. х %3D zo + и m