Question

According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was $ 110.66 . Assume the amounts are normally distributed with standard deviation $ 20.00 . (a) Find the 7 th percentile of the bill amounts. (b) Find the 65 th percentile of the bill amounts. (c) Find the median of the bill amounts.

Answer 1

Solution:-

Given that,

mean = = 110.66

standard deviation = = 20.00

a) Using standard normal table,

P(Z < z) = 7%

= P(Z < z ) = 0.07

= P(Z < -1.48 ) = 0.07  

z = -1.48

Using z-score formula,

x = z * +

x = -1.48 * 20.00 + 110.66

x = $ 81.06

b) Using standard normal table,

P(Z < z) = 65%

= P(Z < z ) = 0.65

= P(Z < 0.39) = 0.65

z = 0.39

Using z-score formula,

x = z * +

x = 0.39 * 20.00 + 110.66

x = $ 118.46

c) Using standard normal table,

P(Z < z) = 50%

= P(Z < z ) = 0.50

= P(Z < 0 ) = 0.50

z = 0

Using z-score formula,

x = z * +

x = 0 * 20.00 + 110.66

x = $ 110.66