Answer:
Step-by-step explanation:
Since the the production of the polymer fiber follows a normal distribution, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = measured diameter values.
µ = mean diameter
σ = standard deviation
From the information given,
µ = 30 μm
σ = 20 μm
a) The probability of a measured value greater than 80 μm is expressed as
P(x > 80) = 1 - P(x ≤ 80)
For x = 80,
z = (80 - 30)/20 = 2.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.994
P(x > 80) = 1 - 0.994 = 0.006
b) the probability of a measured value between 60 and 75 μm is expressed as
P(60 ≤ x ≤ 75)
For x = 60,
z = (60 - 30)/20 = 1.5
The probability corresponding to the z score is 0.933
For x = 75,
z = (75 - 30)/20 = 2.25
The probability corresponding to the z score is 0.988
Therefore,
P(60 ≤ x ≤ 75) = 0.988 - 0.933 = 0.055
