Question

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

Answer 1

Answer:

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