Statistics Homework

Question

he Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 40 ounces and a standard deviation of 8 ounces.

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

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

a) 68% of the widget weights lie between

and

b) What percentage of the widget weights lie between 24 and 48 ounces?

%

c) What percentage of the widget weights lie below 64%

Answer 1

mean =40

standard deviation = 8

a) 68% percent fall within 1 standard deviation from the mean, using the empirical rule 68-95-99.7

68% fall in the interval (32,48)

b) 40-24 = 16

16/8 = 2 = z score = 2 standard deviations below the mean using the empirical rule 95% are within 2 standard deviations fro the mean. but you want only half that.

24 to 40 is .95/2 = 47.5%

c) below 64 would mean z=(64-40)/8 = 24/8 = 3 standard devations above the mean

99.7% + (100-99.7)/2 = 99.7% + .3/2 = 99.7+.15 =99.85%