A manufacturer makes integrated circuits that each have a resistance layer with a target thickness of 200 units. A circuit won't work well if this thickness varies too much from the target value. These thickness measurements are approximately normally distributed with a mean of 200 units and a standard deviation of 12 units. A random sample of 16 measurements is selected for a quality inspection. We can assume that the measurements in the sample are independent.
What is the probability that the mean thickness in these 16 measurements xˉ is farther than 3 units away from the target value?

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. : 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

=

.32

Step-by-step explanation:

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it has to have an angle of 90 degrees