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
This problem uses the Empirical Rule (also known as the 68-95-99.7 rule) for normal distributions. This rule states that for a normal distribution: Approximately 68% of the data falls within 1 standard deviation of the mean. Approximately 95% of the data falls within 2 standard deviations of the mean. Approximately 99.7% of the data falls within 3 standard deviations of the mean. We are given: Mean () = 15 Standard deviation () = 3 We need to find the interval that includes about 95% of the probability. According to the Empirical Rule, this interval is ± 2. Step 1: Calculate the lower bound of the interval. Lower bound = - 2 = 15 - 2(3) = 15 - 6 = 9 Step 2: Calculate the upper bound of the interval. Upper bound = + 2 = 15 + 2(3) = 15 + 6 = 21 The interval that includes about 95% of the probability is 9-21. Comparing this result with the given options: a) 12-18 b) 9-21 c) 6-24 d) 3-27 e) none of the above The calculated interval matches option (b). The final answer is b) 9-21. Got more? Send 'em!