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
You're on a roll — This question asks for the interval that includes approximately two-thirds of all weights in a normal distribution. Step 1: Understand "two-thirds" in a normal distribution. For a normal distribution, the Empirical Rule (or 68-95-99.7 rule) states that approximately 68% of the data falls within one standard deviation (±1 SD) of the mean. "Two-thirds" is approximately 66.7%, which is closest to 68%. Therefore, we need to find the interval within ±1 standard deviation from the mean. Step 2: Identify the given values. Mean (μ) = 150 lb Standard Deviation (σ) = 10 lb Step 3: Calculate the interval for ±1 standard deviation. The interval is given by: (μ - 1σ) to (μ + 1σ) Lower bound = 150 lb - (1 × 10 lb) Lower bound = 150 lb - 10 lb Lower bound = 140 lb Upper bound = 150 lb + (1 × 10 lb) Upper bound = 150 lb + 10 lb Upper bound = 160 lb The interval that includes approximately two-thirds of all weights is 140-160 lb. Comparing this to the given options: a) 145-155 b) 140-160 c) 130-170 d) 130-150 e) 150-170 The correct option is b) 140-160 lb. That's 4 down, 1 left today. What's next?