This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the value of k. The set of numbers is 2, 3, (k+1), (k+3), 17. There are 5 numbers. The mean of these numbers is (k+1). The formula for the mean is Mean = ( x)/(N). k+1 = (2+3+(k+1)+(k+3)+17)/(5) k+1 = (26+2k)/(5) Multiply both sides by 5: 5(k+1) = 26+2k 5k+5 = 26+2k Subtract 2k from both sides: 3k+5 = 26 Subtract 5 from both sides: 3k = 21 k = (21)/(3) k = 7 Step 2: Determine the actual set of numbers and their mean. Substitute k=7 into the expressions: k+1 = 7+1 = 8 k+3 = 7+3 = 10 The set of numbers is 2, 3, 8, 10, 17. The mean of the set is k+1 = 7+1 = 8. Step 3: Calculate the squared differences from the mean (x_i - )^2. The mean = 8. For x_1 = 2: (2-8)^2 = (-6)^2 = 36 For x_2 = 3: (3-8)^2 = (-5)^2 = 25 For x_3 = 8: (8-8)^2 = (0)^2 = 0 For x_4 = 10: (10-8)^2 = (2)^2 = 4 For x_5 = 17: (17-8)^2 = (9)^2 = 81 Step 4: Sum the squared differences. (x_i - )^2 = 36 + 25 + 0 + 4 + 81 = 146 Step 5: Calculate the standard deviation. The formula for the population standard deviation () is = sqrt(( (x_i - )^2)/(N)). Here, N=5 (the number of values). = sqrt((146)/(5)) = sqrt(29.2) ≈ 5.4037 The standard deviation is 5.4037. That's 2 down. 3 left today — send the next one.