Question

h1. The monthly electric bill for a household in the United States is normally distributed with ?= $100 and ?=$20 (Source: US Energy Information Agency)

Deko wonders how much her typical monthly electric bill will be. What would you advise her to expect?  

Provide a comprehensive answer that uses statistical concepts and computations from normal curves including the Empirical Rule and Z scores.

Answer 1

Mean, = $100

Standard deviation, = $20

The value range under one standard from the mean is $80 to $120

The value range under two standard deviations from the mean is $60 to $140

From Empirical rule for normal distribution, 68% of the values lies within one standard deviation from mean.

and 95% of the values lies within two standard deviations from mean.

With 68% chance, the bill can be expected to be in the range of $80 to $120

and with 95% chance, the bill can be expected to be in the range of $60 to $140

with 99.7% chance, the bill can be expected to be in the range of $40 to $160