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The length of life of oil-drilling bits depends upon the
Chapter 4, Problem 164SE(choose chapter or problem)
Problem 164SE
The length of life of oil-drilling bits depends upon the types of rock and soil that the drill encounters, but it is estimated that the mean length of life is 75 hours. An oil exploration company purchases drill bits whose length of life is approximately normally distributed with mean 75 hours and standard deviation 12 hours. What proportion of the company’s drill bits
a will fail before 60 hours of use?
b will last at least 60 hours?
c will have to be replaced after more than 90 hours of use?
Questions & Answers
QUESTION:
Problem 164SE
The length of life of oil-drilling bits depends upon the types of rock and soil that the drill encounters, but it is estimated that the mean length of life is 75 hours. An oil exploration company purchases drill bits whose length of life is approximately normally distributed with mean 75 hours and standard deviation 12 hours. What proportion of the company’s drill bits
a will fail before 60 hours of use?
b will last at least 60 hours?
c will have to be replaced after more than 90 hours of use?
ANSWER:
Solution 164SE
Step1 of 4:
Let us consider a random variable Y it follows normal distribution with mean and standard deviation
Here our goal is:
a). We need to find the proportion of the company’s drill bits will fail before 60 hours of use.
b). We need to find the proportion of the company’s drill bits will last at least 60 hours.
c). We need to find the proportion of the company’s drill bits will have to be replaced after more than 90 hours of use.
Step2 of 4:
a).
We have mean and standard deviation
Consider,
The Z statistics is given by:
Where, is obtained from standard normal table(area under normal curve).
In area under normal curve we have to see in row -1.2 under column 0.05.
Now,