Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 37 ounces and a standard deviation of 6 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 and b) What percentage of the widget weights lie between 19 and 49 ounces? % c) What percentage of the widget weights lie above 31 ? % Get help: Video LicensePoints possible: 2

Answer 1

mean = 37

sd = 6

Assuming that the data is normally distributed, as per Empirircal rule :

Approx. 68% of the data lies between mean ± 1 SD, or between 31 and 43

Approx. 95% of the data lies between mean ± 2 SD, or between 25 and 49

Approx. 99.7% of the data lies between mean ± 3 SD, or between 19 and 55

a) 95% of the widget weights lie between :

37 + /- 12 = 25 and 49

ANS: 25 and 49

b) What percentage of the widget weights lie between 19 and 49 ounces?

As 99.7% of the data lies between mean ± 3 SD, or between 19 and 55

49.85% of the data lies between 19 and 37 (mean)

As 95% of the data lies between mean ± 2 SD, or between 25 and 49

47.50% of the data lies between 37 and 49

Hence daa between 19 and 49 = 49.85% + 47.50% = 97.35%

ANS : 97.35%

c) What percentage of the widget weights lie above 31 ?

As 68% of the data lies between mean ± 1 SD, or between 31 and 43;

34% of the data lies between 31 to 37

Data above 37 (i.e. right side of the graph = 50% as the data is normally distributed)

Hence data above 31 = 34% + 50% = 84%

ANS: 84%