The photoresist thickness in semiconductor manufacturing has a mean of 10 microm

Question

The photoresist thickness in semiconductor manufacturing has a mean of 10 micrometers and a standard deviation of 1 micrometer. Assume that the thickness is normally distributed and that the thicknesses of different wafers are independent. Round your answer to four decimal places (e.g. 98.7654).

Determine the probability that the average thickness of 10 wafers is either greater than 12 or less than 9 micrometers.

Please explain how I would put this in TI-84 Plus. Not allowed to use excell during test, and this is a test prep question. THANKS!

Explanation / Answer

Solution:

We are given

Mean = µ = 10 and SD = = 1

Sample size = n = 10

We have to find P(Xbar>12) + P(Xbar<9)

First we have to find P(Xbar>12)

P(Xbar>12) = 1 – P(Xbar<12)

Z = (Xbar = µ) / [ /sqrt(n)]

Z = (12 – 10) / [1/sqrt(10)]

Z = 6.324555

P(Xbar<12) = P(Z< 6.324555) = 1.000

P(Xbar>12) = 1 – P(Xbar<12)

P(Xbar>12) = 1 – 1 = 0.00

Now, we have to find P(Xbar<9)

Z = (9 – 10) / [1/sqrt(10)]

Z = -3.16228

P(Xbar<9) = P(Z< -3.16228) = 0.000783

P(Xbar>12) + P(Xbar<9) = 0.00 + 0.000783 = 0.000783

Required probability = 0.0008

Ti-84 instructions:

Press 2nd VARS [DISTR]

Scroll down to

2:normalcdf(

Press ENTER

Enter -3.16228, 6.324555)

And press ENTER

Then subtract this answer from 1 to get required probability.

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