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# The amount of warpage in a type of wafer used in the

ISBN: 9780073401331 38

## Solution for problem 6E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Problem 6E

The amount of warpage in a type of wafer used in the manufacture of integrated circuits has mean 1.3 mm and standard deviation 0.1 mm. A random sample of 200 wafers is drawn.

a. What is the probability that the sample mean warpage exceeds 1.305 mm?

b. Find the 25th percentile of the sample mean.

c. How many wafers must be sampled so that the probability is 0.05 that the sample mean exceeds 1.305?

Step-by-Step Solution:

Answer:

Step 1 of 3:

(a)

In this question, we are asked to find the probability that the sample mean warpage exceeds 1.305.

The amount of warpage in a type of wafer used in the manufacture of integrated circuits has mean 1.3and standard deviation 0.1.

A random sample of 200 wafers is drawn.

Let represent amount of warpage.

We need to find

Now the sample size is , which is a large sample.

Hence  can be approximately normal distributed.

CLT specifies that , variance  and standard deviation

Hence our sample mean and standard deviation is,

= 7.07

Therefore the  score of  1.305 is

=

=

=

From the z table, the area to the left of   is 0.7794

= 1 - the area to the left of

= 1 - 0.7794

= 0.2206

Hence the probability that the sample mean warpage exceeds 1.305is 0.2206.

Step 2 of 3

Step 3 of 3

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