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
Here are the solutions to the problems: 62. If b = 2 and a = 5, predict y when x = 4 Assuming the linear prediction equation is y = a + bx. Step 1: Substitute the given values into the equation. y = 5 + (2)(4) Step 2: Perform the multiplication. y = 5 + 8 Step 3: Perform the addition. y = 13 The predicted value of y is 13. The correct option is C. C. 13 63. Class size: Range = 50, K = 5 The formula for class size (or class width) is given by: Class Size = RangeK Step 1: Substitute the given values. Class Size = (50)/(5) Step 2: Calculate the class size. Class Size = 10 The class size is 10. The correct option is B. B. 10 64. Sturges: N = 64 Sturges' formula for the number of classes (K) is: K = 1 + 3.322 _10(N) Step 1: Substitute N = 64 into the formula. K = 1 + 3.322 _10(64) Step 2: Calculate the value of _10(64). _10(64) ≈ 1.80618 Step 3: Substitute the log value back into the formula and calculate K. K = 1 + 3.322 × 1.80618 K = 1 + 5.99999 K ≈ 7.0 The number of classes is approximately 7. The question asks for "Sturges: N=64" and provides options. Option B is the formula itself, which evaluates to approximately 7. The correct option is B. B. 1 + 3.322 64 65. CI: x = 50, = 10, n = 25, Z = 1.96. Margin of error = The formula for the margin of error (ME) for a confidence interval for the mean when the population standard deviation () is known is: ME = Z · ()/(sqrt(n)) Step 1: Substitute the given values into the formula. ME = 1.96 · (10)/(sqrt(25)) Step 2: Calculate the square root of n. ME = 1.96 · (10)/(5) Step 3: Perform the division. ME = 1.96 · 2 Step 4: Perform the multiplication. ME = 3.92 The margin of error is 3.92. The correct option is B. B. 3.92 66. CI interval = 50 ± 3.92 The confidence interval (CI) is given by x ± ME. Given: x = 50 and ME = 3.92. Step 1: Calculate the lower bound of the interval. Lower Bound = x - ME = 50 - 3.92 = 46.08 Step 2: Calculate the upper bound of the interval. Upper Bound = x + ME = 50 + 3.92 = 53.92 The confidence interval is (46.08, 53.92). The correct option is A. A. (46.08, 53.92)