×
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.5 - Problem 20e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.5 - Problem 20e

×

# The quality-assurance program for a certain adhesive

ISBN: 9780073401331 38

## Solution for problem 20E Chapter 4.5

Statistics for Engineers and Scientists | 4th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Statistics for Engineers and Scientists | 4th Edition

4 5 1 276 Reviews
10
5
Problem 20E

The quality-assurance program for a certain adhesive formulation process involves measuring how well the adhesive sticks a piece of plastic to a glass surface. When the process is functioning correctly, the adhesive strength X is normally distributed with a mean of 200 N and a standard deviation of 10 N. Each hour, you make one measurement of the adhesive strength. You are supposed to inform your supervisor if your measurement indicates that the process has strayed from its target distribution.

a. Find P(X ≤ 160), under the assumption that the process is functioning correctly.

b. Based on your answer to part (a), if the process is functioning correctly, would a strength of 160 N be unusually small? Explain.

c. If you observed an adhesive strength of 160 N, would this be convincing evidence that the process was no longer functioning correctly? Explain.

d. Find P(X  ≥ 203), under the assumption that the process is functioning correctly.

e. Based on your answer to part (d), if the process is functioning correctly, would a strength of 203 N be unusually large? Explain.

f. If you observed an adhesive strength of 203 N, would this be convincing evidence that the process was no longer functioning correctly? Explain.

g. Find P(X  ≤ 195), under the assumption that the process is functioning correctly.

h. Based on your answer to part (g), if the process is functioning correctly, would a strength of 195 N be unusually small? Explain.

i. If you observed an adhesive strength of 195 N, would this be convincing evidence that the process was no longer functioning correctly? Explain.

Step-by-Step Solution:

Step 1 of 9:

(a)

In this question, we are asked to find , under the assumption that the process is functioning correctly.

When the process is functioning correctly, the adhesive strength  is normally distributed with a mean of  and a standard deviation of  10.

We need to find .

Here we can write,

Now we will calculate the  score because our distribution is approximately normal.

The z-score of 160 is z  =

From the z table, the area to the left of  is negligible.

Therefore  .

Step 2 of 9

Step 3 of 9

## Discover and learn what students are asking

Calculus: Early Transcendental Functions : Linear Models and Rates of Change
?In Exercises 5-10, plot the pair of points and find the slope of the line passing through them. (1,1), (-2,7)

Calculus: Early Transcendental Functions : The Natural Logarithmic Function: Integration
?In Exercises 1-26, find the indefinite integral. $$\int \frac{1}{x+1} d x$$

Statistics: Informed Decisions Using Data : Scatter Diagrams and Correlation
?True or False: Correlation implies causation.

Statistics: Informed Decisions Using Data : Inference about the Difference between Two Medians: Dependent Samples
?In Problems 3–10, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent sa

Chemistry: The Central Science : Chemical Reactions and Reaction Stoichiometry
?A compound whose empirical formula is $$\mathrm{XF}_{3}$$ consists of 65 % F by mass. What is the atomic mass of X ?

#### Related chapters

Unlock Textbook Solution