Probabilities are used to determine the chances of events
The value of the probability P(x < 24) is 0.7895
<h3>How to calculate the probability P(x < 24)?</h3>This is calculated as:
So, we have:
Evaluate the sums
Evaluate the quotient
Hence, the value of the probability P(x < 24) is 0.7895
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Complete Question
A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of parts had a mean of 1.6 millimeters with a standard deviation of 0.03 millimeters. what standard deviation will be needed to achieve a process capability index f 2.0?
Answer:
The value required is
Step-by-step explanation:
From the question we are told that
The upper specification is
The lower specification is
The sample mean is
The standard deviation is
Generally the capability index in mathematically represented as
Now what min means is that the value of CPk is the minimum between the value is the bracket
substituting value given in the question
=>
So
Now from the question we are asked to evaluated the value of standard deviation that will produce a capability index of 2
Now let assuming that
So
=>
=>
So
=>
Hence
So
So is the value of standard deviation required