Answer:
0.3174
Step-by-step explanation:
Given that a manufacturer makes integrated circuits that each have a resistance layer with a target thickness of 200 units
These thickness measurements, X, are approximately normally distributed with a mean of 200 units and a standard deviation of 12 units.
Sample size n = 16
Sample mean will follow N(mu = 200, std error = 12/sqrt 16)
i.e. [tex]\bar X[/tex]: N(200, 3)
Required probability
= probability that the mean thickness in these 16 measurements xˉ is farther than 3 units away from the target value
= [tex]P(|bar x-200|>3)\\=P(|z|>1)\\= 1-0.6826\\= 0.3174[/tex]
