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 ?  %

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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 ?  %

 

  

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Expert Answer

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,

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t3046 3(6) (46-18,46+18) (28,64)

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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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to46 (6) (46-6,46+6) =(40,52)

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