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: State the Taro Yamane formula and given values. The Taro Yamane formula for sample size (n) for finite populations is: n = (N)/(1 + N(e^2)) Where: N = Population size e = Level of precision Given values from the problem: N = 1,771,094 e = 0.05 Step 2: Substitute the given values into the formula. Substitute N = 1,771,094 and e = 0.05 into the formula: n = (1,771,094)/(1 + 1,771,094(0.05^2)) Step 3: Calculate the square of the level of precision (e^2). e^2 = (0.05)^2 = 0.0025 Substitute this back into the equation: n = (1,771,094)/(1 + 1,771,094(0.0025)) Step 4: Multiply the population size by e^2. 1,771,094 × 0.0025 = 4427.735 Substitute this back into the equation: n = (1,771,094)/(1 + 4427.735) Step 5: Add 1 to the result from Step 4. 1 + 4427.735 = 4428.735 Substitute this back into the equation: n = (1,771,094)/(4428.735) Step 6: Divide the population size by the denominator. n = (1,771,094)/(4428.735) ≈ 399.9099 Step 7: Round the sample size to the nearest whole number. Since the sample size must be a whole number, round 399.9099 to the nearest integer. n ≈ 400 The calculations shown in the image are correct. The final calculated sample size is 400. That's 2 down. 3 left today — send the next one.