Question

The mean monthly utility bill for a simple of household in a city is $139.25 with a standard deviation of $14.54. Find the range of values in which at least 75% of the monthly utility bills lie.

Answer 1

Solution:-

Given that,

mean = = $ 139.25

standard deviation = = $ 14.54

Using standard normal table,

P(Z > z) = 75%

= 1 - P(Z < z) = 0.75  

= P(Z < z) = 1 - 0.75

= P(Z < z ) = 0.25

= P(Z < -0.6745 ) = 0.25  

z = -0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 14.54 + 139.25

x = $ 129.44

Using standard normal table,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.6745) = 0.75

z = 0.6745

Using z-score formula,

x = z * +

x = 0.6745 * 14.54 + 139.25

x = $ 149.06

The 75% range of values is $ 129.44 and $ 149.06