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The quality-assurance program for a certain adhesive
Chapter 4, Problem 20E(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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.
ANSWER:
Answer:
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
.