Answer: P(271 ≤ x ≤ 273) is 0.29
Explanation:
Since Furnace repair bills are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ/√n
Where
x = furnace repair bills
µ = mean
σ = standard deviation
n represents number of samples
From the information given,
µ = 271 dollars
σ = 20 dollars
n = 64
The probability that they have a mean cost between 271 dollars and 273 dollars is expressed as
P(271 ≤ x ≤ 273)
For x = 22,
z = (271 - 271)/(20/√64) = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 273
z = (273 - 271)/(20/√64) = 0.8
Looking at the normal distribution table, the probability corresponding to the z score is 0.79
Therefore,
P(271 ≤ x ≤ 273) = 0.79 - 0.5 = 0.29