Math Problem Statement
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearings can operate are 0.73 inch and 0.77 inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.754 inch and a standard deviation of 0.007 inch. Complete parts (a) through (e) below. Question content area bottom 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.) Part 2 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.) Part 3 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.) Part 4 d. What is the probability that a ball bearing is below the lower specification limit? 0.0003 (Round to four decimal places as needed.) Part 5 e. Of all the ball bearings, 91% of the diameters are greater than what value? 0.745 inch (Round to three decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Normal Distribution
Z-scores
Formulas
Z = (X - μ) / σ
P(a < X < b) = P((a - μ) / σ < Z < (b - μ) / σ)
Theorems
Empirical Rule
68-95-99.7 Rule
Suitable Grade Level
Undergraduate / Advanced High School