Concept explainers
(a)
To explain: The reason behind assuming that the cap strength and torque applied by machine is independent.
(a)
Explanation of Solution
Given:
T denotes the capping machine torque
C denotes the cap strength
Both of them follow
Mean of T
Standard deviation of T
Mean of C
Standard deviation of C
Formula used:
When two
Both the torque capping machine and caps on containers are different machines and strength applied are working independently.
So, both of them are working independently.
(b)
To find: The mean and standard deviation of D
(b)
Answer to Problem 4CRE
Explanation of Solution
Calculation:
Using the given information as stated in sub part a
Both T and C are independent, so
So,
(c)
To find: Probability that a cap will break during fastening.
(c)
Answer to Problem 4CRE
The probability is 0.2275.
Explanation of Solution
Calculation:
From sub part b
The cap breaks while fastening means that the strength of the cap is less than that of the capping machine torque, so the probability can be calculated as follows
Finding the probability
Reading from z tables
Thus, the required probability is 0.02275.
Chapter 6 Solutions
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