Question

The Acme Company manufactures widgets. The distribution of widget weights is bell shaped. The widget weights have a mean of 39 ounces and a standard deviation of 4 ounces.

use the empirical rule.

A) 95% of the widget weights lie between ___ and _____

B) what percentage of the widget weights lie between 35 and 47 ounces? ______%

C) what percentage of the widget weight slide below 51? ____________%

Answer 1

The distribution of widget weights is bell shaped. The widget weights have a mean of 39 ounces and a standard deviation of 4 ounces.

By emperical rule,

A) We know 95% of data lies within 2 standard deviation.

   = (39-2*4 , 39+2*4) = (31 , 47)

95% of the widget weights lie between 31 and 47.

B) percentage of the widget weights lie between 35 and 47 ounces,

we know,

Putting x = 35 and 47 we get,

  

P(-1 < z < 2) = 0.8186

Hence, percentage of the widget weights lie between 35 and 47 ounces is 81.86%

C) percentage of the widget weight slide below 51

  

P( Z < 3) = 0.9987

percentage of the widget weight slide below 51 is 99.87%

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