Direction: Solve the given real - life problem below. Show the complete solution for the following Score: tasks. Problem: As a Physical Education teacher of Lauis National High School Senior High School, Ma'am Mary Joseph wants to compute for the Body Mass Index of few students as part of her research. As a start, the table below shows the heights of five students in meters. Supposed samples of size 2 are taken from this population of five students, complete the given table and answer the following tasks. Construct the desired tables needed for your solutions and answers. Student Height In Meters (X) X2 Hazel Kim 1.47 2.16 Mee Ann Mae 1.58 2.50 Grace Ann 1.67 2.79 Jethro 1.69 2.86 Chelsea Mae 1.51 2.28 TOTAL 7.92 12.59 1. Solve for the mean of the population u. 2. Solve for the mean of the sampling distribution of the sample means ux. Possible Sample Sample Mean Sample Frequency Probability X . P(X) (size 2) (X) Mean (X) P(X) 3. Compare u and ux. 4. Solve for the variance (62) and the standard deviation (o) of the population. Use the given data above. Standard Deviation: 6 = EX - (Ex) Variance: 02 = EX ( Ex ) N 5. Solve the variance (63) and the standard deviation (ox) of the sampling distribution of the sample means ur.99./ 10 D. 100% B. Compute the following probabilities using the standard normal curve. Construct a curve then shade the region corresponding to the area.. 11 - 15. P(Z > -2.53) C. Complete the table by converting the given values into z-scores. Then find the corresponding area using the z-table. Given Z - score Approximate Value 16 - 20. x = 28 H = 16 0 =5Solve for the mean of the sampling distribution of the sample means us. Possible Sample Sample Mean (size 2) (X) Sample Frequency Mean (X) Probability (X) X . P(X ) 3. Compare u and US. 4. Solve for the variance (a?) and the standard deviation (a) of the population. Use the given data above. Variance: Standard Deviation: 0 = Ex - () 5. Solve the variance (637 and the standard deviation (ox) of the sampling distribution of the sample means uli o'= = [[X2 . P(X)] - 17, Of = [[X2 . P(X)] - 3x 6. Compare o and Of. Rubrics: Distinguished Proficient Apprentice Novice 3 Identifies special factors Understands the problem Understands enough to Doesn't understand enough Understand the Problem that influences the solve part of the problem or to get started of make approach before starting get part of the solution progress the problem Explains why certain Lises all appropriate Uses some appropriate Uses inappropriate Uses Information information is essential to information correctly information correctly Information Appropriately the solution Explains why procedures Applies completely Apples some appropriate Applies Inapproprite Applies Appropriate are appropriate for the appropriate procedures procedures procedures Procedures problem Uses a representation that is Uses a representation that Uses a representation that Uses a representation that unusual in its mathematical clearly depicts the problem gives some important gives little or no significant Uses Representation nreckann information cho it the Information chal d the