The mean monthly bill for a sample of households in a city is $70, with a standard deviation of $8.

Using this data, let us assume that the number of households is 40

a. Estimate the number of households whose monthly utility bills are between $54 and $86

b. In a sample of 20 additional households, about how many households would you expect to have monthly utility bills between $54 and $86.

a) 39

b) 58

Explanation:

Data provided in the question:

Mean = $70

Standard deviation, s = $8

Number of households, n = 40

Now,

a) number of households whose monthly utility bills are between $54 and $86

z score for $54 = [ 54 - 70 ] : 8 [ z score = [ X - mean ] : s]

or

z score for $54 = - 2

z score for $86 = [ 86 - 70 ] : 8 [ z score = [ X - mean ] : s]

or

z score for $54 = 2

Therefore,

P (between $54 and $86) = P (z = 2) - P (z = - 2)

= 0.9772498 - 0.0227501

= 0.9544997

Therefore,

number of households whose monthly utility bills are between $54 and $86

= P (between $54 and $86) * n

= 0.9544997 * 40

= 38.18 ≈ 39

b) In a sample of 20 additional house i. e n' = 40 + 20 = 60

thus,

number of households whose monthly utility bills are between $54 and $86

= P (between $54 and $86) * n'

= 0.9544997 * 60

= 57.27 ≈ 58