The data represent the capacity of fruit juice (in litres) in 8 different Containers arranged in ascending order: Pt 4, 11, 12, 15, 3p-1, 1p-2, 27, P2-6. a) If the range is 20, find the i) value of P, ii) Mean of Distribution.

The given data points, arranged in ascending order, are: P+4, 11, 12, 15, 3P-1, 4P-2, 27, P^2-6 a) i) Value of P Step 1: Use the definition of range. The range is the difference between the maximum and minimum values. Since the data is in ascending order, the minimum value is P+4 and the maximum value is P^2-6. The given range is 20. Range = Maximum Value - Minimum Value 20 = (P^2-6) - (P+4) 20 = P^2 - 6 - P - 4 20 = P^2 - P - 10 Step 2: Solve the quadratic equation for P. Rearrange the equation to form a standard quadratic equation: P^2 - P - 10 - 20 = 0 P^2 - P - 30 = 0 Factor the quadratic equation: (P-6)(P+5) = 0 This gives two possible values for P: P=6 or P=-5. Step 3: Validate the values of P based on the ascending order of the data. If P=6, the data points are: 6+4 = 10 11 12 15 3(6)-1 = 18-1 = 17 4(6)-2 = 24-2 = 22 27 (6)^2-6 = 36-6 = 30 The sequence is 10, 11, 12, 15, 17, 22, 27, 30. This is in ascending order. If P=-5, the data points are: -5+4 = -1 11 12 15 3(-5)-1 = -15-1 = -16 4(-5)-2 = -20-2 = -22 27 (-5)^2-6 = 25-6 = 19 The sequence is -1, 11, 12, 15, -16, -22, 27, 19. This is not in ascending order (e.g., 15 > -16). Therefore, P=-5 is not a valid solution. The value of P is 6. a) ii) Mean of distribution Step 4: List the data points using the valid value of P=6. The data points are: 10, 11, 12, 15, 17, 22, 27, 30. The number of data points is n=8. Step 5: Calculate the sum of the data points. Sum = 10+11+12+15+17+22+27+30 Sum = 144 Step 6: Calculate the mean of the distribution. Mean = Sum of data pointsNumber of data points Mean = (144)/(8) Mean = 18 The mean of the distribution is 18. Send me the next one 📸