Could I get this answer and explanation of this question? Thank you.

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 65 ounces and a standard deviation of 4 ounces.

Use the Empirical Rule, find

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

b) What percentage of the widget weights lie between 61 and 73 ounces? _____ %

c) What percentage of the widget weights lie below 77 ? ________ %

Answer 1

a) between 57 and 73 are 95%. 65 +/-2(4) =65-8 to 65-8= mean +/-2 standard devations

b) between 61 to 73 are 68/2+ 95/2 = 34+47.5 = 81 1/2 %

c) below 77 is 1-99.7 = 0.3%/2= 0.15%, below 3 standard deviations above the mean = 3/20 of 1%

Answer 2

95% of the weights lies within 2 standard deviations of the mean: 65 - 2*4, 65 + 2.4 = 57,73

61 is one standard deviation below the mean. 34% of the data is between one standard deviation below the mean and the mean. 73 is two standard deviations above the mean. 47.5% of the data is between the mean and two standard deviations above the mean. So in total 34 + 47.5 = 81.5% of the data lies between 61 and 73.

77 is 3 standard deviations above the mean. All but 0.15% of the data lies below 3 standard deviations above the mean so 1 - 0.15 = 99.85% of the data lies below 77.