10. A process manufactures ball bearings with diameters that are normally distributed with mean 25.1 millimeters and standard deviation 0.08 millimeter. a. [5pts] What proportions of the diameters are greater than 25.4? Answer: a. [5pts] To meet a certain specification, a ball bearing must have a diameter between 25.0 and 25.3 millimeters. What proportions of the ball bearings meet specification? Answer: a. [5pts] Find the 95th percentile of the diameters. Answer:
Added by Kimberly G.
Close
Step 1
4, we calculate: \[ P(X > 25.4) = 1 - P(X \leq 25.4) = 1 - P\left(\frac{X - \mu}{\sigma} \leq \frac{25.4 - 25.1}{0.08}\) \[ = 1 - P(Z \leq 3.75) = 1 - 0.9999 = 0.0001 \] Show more…
Show all steps
Your feedback will help us improve your experience
Aarti Kumari and 60 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A process manufactures ball bearings with diameters that are normally distributed with a mean of 25.1 millimeters and a standard deviation of 0.08 millimeters. What proportion of the diameters are less than 25.0 millimeters? What proportions of the diameters are greater than 25.4? To meet a certain specification, a ball bearing must have a diameter between 25.0 and 25.3 millimeters. What proportions of the ball bearings meet specification? Find the 95th percentile of the diameters.
Avi Z.
A process manufactures ball bearings with diameters that are normally distributed with mean 25.15 mm and standard deviation 0.08 mm. A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on? (Round up the final answer to the nearest whole number.) A diameter of 25.2 mm is on the__ th percentile, approximately.
Ahmet Y.
A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 500 in. A bearing is acceptable if its diameter is within. 004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with mean value .499 in. and standard deviation. 002 in. What percentage of the bearings produced will not be acceptable?
Continuous Random Variables and Probability Distributions
The Normal (Gaussian) Distribution
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD