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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.11 - Problem 6e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.11 - Problem 6e

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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:

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 1.3 and 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 1.305 is 0.2206.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

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