The acme company manufactures widgets. the distribution of widget weights is bell-shaped. the widget weights have a mean of 55 ounces and a standard deviation of 8 ounces. use the empirical rule. suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between and b) what percentage of the widget weights lie between 39 and 79 ounces? % c) what percentage of the widget weights lie below 63 ? %

a) 31 and 79 b) 97.35% c) 84%

Step-by-step explanation:

If we are going to use the empirical rule, we should use the normal probability density function. We have a mean of =55 ounces and a standard deviation of =8 ounces. Let's compute the following figures

= 55-8=47

= 55-2(8)=39

= 55-3(8)=31

= 55+8=63

= 55+2(8)=71

= 55+3(8)=79

The empirical rule is shown in the image.

a) 99.7% of the widget weights lie between 31 and 79. 31 is the mean minus 3 standard deviations and 79 is the mean plus 3 standard deviations.

b) Between 39 and 71 lie 95%  of the widget weights, and between 71 and 79 lie 2.35% of the widget weights, therefore, between 39 and 79 lie 95%+2.35%=97.35% of the widget weights.

c) Below 55 lie 50% of the widget weights and between 55 and 63 lie 34% of the widget weights, therefore, below 63 lie 84% of the widget weights.

- 70

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12.5 feet

step-by-step explanation: