Question

Asked Nov 18, 2019

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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 6 ounces.**Use the Standard Deviation Rule, also known as the Empirical Rule (see image below)**. Do not use normalcdf on your calculator.

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 40 and 64 ounces? %

c) What percentage of the widget weights lie below 58 ? %

Step 1

It is given that the widget weights follows normal distribution with mean of 46 and standard deviation of 6.

*Empirical rule:*

- About 68% of data lies within the first standard deviation of the mean.
- About 95% of the data lies within the two standard deviations of the mean.
- About 99.7% of the data lies within the three standard deviations of the mean.

Step 2

**(a)**

From the empirical rule, it can be observed that 99.7% of the data lies within the three standard deviations of the mean. Therefore,

Step 3

Hence, 99.7% of the widget weights lie between **28 and 64**.

**b)**

The widget weights for one stand...

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