Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 62 ounces and a standard deviation of 3 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 95% of the widget weights lie between blank and blank

b) What percentage of the widget weights lie between 59 and 68 ounces?

c) What percentage of the widget weights lie above 53 ?

Answer 1

Given

One standard deviation :

Two standard deviations :

Two standard deviations :

The empirical rule states that of the distribution lies within two standard deviations.

a) So the of the widget weights lie between .

b)

Define

We use empirical rule to calculate the

The rule states that of the data lies between one standard deviations

thus

The rule states that of the data lies between the two standard deviations.

Thus

So the

The percentage of the widget weights that lie between 59 and 68 hours is .

c)

The empirical rule states that 99.7% of the data is between 3 standard deviations,

It means that lies outside the 3 standard deviations on both the side

So the percentage of the widget weights that lie above 53 is