The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 3 ounces.

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 3 ounces

b) What percentage of the widget weights lie between 41 and 53 ounces? Incorrect

c) What percentage of the widget weights lie below 56 ? Incorrect

Answer 1

mean = 50

sd = 3

41 is 3 sd below the mean 50-3(3) =50-9=41

53 is 1 sd above the mean

by the empirical rule 68-95-99.7

68/2 = 34 are above the mean for 1 sd

99.7/2 = 49.85 below the mean for 3 sd

49.85+34 = 83.85% are between 41 and 53

56 is 2 sd above the mean

95/2 = 47.5 between 50 and 56

add 50 for below 50

50+47.5 = 97.5% are below 56