Part 1 a. What is the probability that a ball bearing is between the target and the actual​ mean?   enter your response here ​(Round to four decimal places as​ needed.)   b. What is the probability that a ball bearing is between the lower specification limit and the​ target?   enter your response here ​(Round to four decimal places as​ needed.)   c. What is the probability that a ball bearing is above the upper specification​ limit?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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An industrial sewing machine uses ball bearings that are targeted to have a diameter of
0.78
inch. The lower and upper specification limits under which the ball bearings can operate are
0.77
inch and
0.79
​inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally​ distributed, with a mean of
0.783
inch and a standard deviation of
0.003
inch. Complete parts​ (a) through​ (e) below.
 
 
 

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Part 1
a. What is the probability that a ball bearing is between the target and the actual​ mean?
 
enter your response here
​(Round to four decimal places as​ needed.)
 
b. What is the probability that a ball bearing is between the lower specification limit and the​ target?
 
enter your response here
​(Round to four decimal places as​ needed.)
 
c. What is the probability that a ball bearing is above the upper specification​ limit?
 
enter your response here
​(Round to four decimal places as​ needed.)
 
d. What is the probability that a ball bearing is below the lower specification​ limit?
 
enter your response here
​(Round to four decimal places as​ needed.)
 
e. Of all the ball​ bearings,
91​%
of the diameters are greater than what​ value?
 
enter your response here
inch ​(Round to three decimal places as​ needed.)
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