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
