### Acme Company's Widget Weight Distribution AnalysisThe Acme Company manufactures widgets. The widget weights follow a bell-shaped distribution with a mean weight of 59 ounces and a standard deviation of 6 ounces. We will analyze the weight distribution by answering the following questions:a) **99.7% of the widget weights lie between:** - **[ ] and [ ]**b) **What percentage of the widget weights lie between 47 and 77 ounces?** - **[ ] %**c) **What percentage of the widget weights lie below 65 ounces?** - **[ ] %**#### Detailed Analysis:1. **99.7% Range Calculation:** According to the empirical rule for a normal distribution: - 68% of data lies within ±1 standard deviation from the mean. - 95% of data lies within ±2 standard deviations from the mean. - 99.7% of data lies within ±3 standard deviations from the mean. Given the mean (μ) = 59 ounces and standard deviation (σ) = 6 ounces: To find the range for 99.7%: - Lower limit = μ - 3σ = 59 - 18 = 41 ounces - Upper limit = μ + 3σ = 59 + 18 = 77 ounces So, **99.7% of the widget weights lie between 41 and 77 ounces.**2. **Percentage calculation between 47 and 77 ounces:** Using the mean (59 ounces) and standard deviation (6 ounces), calculate z-scores for 47 and 77: - For 47 ounces: \( Z = \frac{47 - 59}{6} = -2 \) - For 77 ounces: \( Z = \frac{77 - 59}{6} = 3 \) Using standard normal distribution tables or a calculator: - The area to the left of z = -2 is approximately 2.5%. - The area to the left of z = 3 is approximately 99.9%. The percentage between z = -2 and z = 3 is \( 99.9 - 2.5 = 97.4\% \). Therefore, **97.4% of the widget weights lie between 47 and 77 ounces.**3. **Percentage

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Description: ### Acme Company's Widget Weight Distribution AnalysisThe Acme Company manufactures widgets. The widget weights follow a bell-shaped distribution with a mean weight of 59 ounces and a standard deviation of 6 ounces. We will analyze the weight distri

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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 59 ounces and a standard deviation of 6 ounces. a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 47 and 77 ounces? c) What percentage of the widget weights lie below 65 ?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 59 ounces and a standard deviation of 6 ounces. a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 47 and 77 ounces? c) What percentage of the widget weights lie below 65 ?

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