The acme company manufactures widgets. the distribution of widget weights is bell-shaped. the widget weights have a mean of 57 ounces and a standard deviation of 8 ounces. use the standard deviation rule, also known as the empirical rule. a) 95% of the widget weights lie b)what percentage of the widget weights lie between 33 and 73 ounces c)what percentage of the widget weights lie above 49

A) The empirical rule says that the 95% of the data falls in between two standard deviations of the mean.

Given : The distribution of widget weights is bell-shaped. i.e. the distribution is a normal distribution.

Population  mean :

Standard deviation :

Then, by empirical rule , 95% of data falls in between

i.e.

Hence, the 95% of the widget weights lie between 41 ounces and 73 ounces .

B) Let x be the random variable that represents the weight of the widgets.

Formula of Z-score :   (1)

Put x= 33 in (1)

Put x= 73 in (1)

Using the standard normal distribution table , we have

P-value :

Hence, 97.59% of the widget weights lie between 33 and 73 ounces .

C) Put x= 49 in (1)

P-value :

Hence, 84.13% of the widget weights lie above 49.

you are saying it as if a fact, not a question, but yes, you would be correct? ; )

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