Answer: P(22 ≤ x ≤ 29) = 0.703
Explanation:
Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = output of the machine in ounces per cup.
µ = mean output
σ = standard deviation
From the information given,
µ = 27
σ = 3
The probability of filling a cup between 22 and 29 ounces is expressed as
P(22 ≤ x ≤ 29)
For x = 22,
z = (22 - 27)/3 = - 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.047
For x = 29,
z = (29 - 27)/3 = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.75
Therefore,
P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703