Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 37 ounces and a standard deviation of 7 ounces. Use the Empirical Rule, also known as the 68-95-99.7 Rule. Do not use Tables or Technology to avoid rounding errors. Suggestion: sketch the distribution in order to answer these questions. a) 68% of the widget weights lie between and b) What percentage of the widget weights lie between 23 and 44 ounces

Answer 1

a) 68 % will lie between 30 and 44 ounces

b) between 23 and 44 ounces will lie 81,5 %

Step-by-step explanation: See Annex

a) Normal Distribution N ( 37, 7)

The Empirical Rule establishes that 68 % of values will be at

μ ± 1 σ where μ is the mean and σ the standard deviation

Then: 37 - 7 = 30 and 37 + 7 = 44

68 % of the values will lie between 30 and 44 ounces

b) And between 23 and 44 we should find:

We have 95 % of values between

μ ± 2*σ

In our case to the left of the value (mean 0 ) and up to the value 23 we get 95/2 = 47,5 % and to the right of the value (mean 0 ) and up to 44 we half 68/2 = 34 %

Then between 23 and 44, we have 47,5 + 34 = 81,5 %