![The Practice of Statistics for AP - 4th Edition](https://www.bartleby.com/isbn_cover_images/9781429245593/9781429245593_largeCoverImage.gif)
(a)
To find: the value of the
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 58E
The mean lid diameter should be 4.00 inches
Explanation of Solution
Given:
The standard deviation remains at
Calculation:
If the standard deviation is 0.2 inches, then it is supposed to find the value of mean diameter that a supplier must set for the large-cup lids to ensure that less than 1% of the lids are too small to fit.
Solve for the appropriate mean so that less than 1% of lids have diameter less than 3.95. First, find the z -value for which 1% of observations are lower. Using standard normal table, find the z value corresponding to
Since this z -value should correspond to a diameter of 3.95,
So the mean lid diameter should be 4.00 inches to ensure that less than 1% of the lids are too small to fit.
Conclusion:
Therefore, the mean lid diameter should be 4.00 inches
(b)
To find: the value of the standard deviation of the lids which are very small to fit.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 58E
It is extremely rare for a lid to be too big.
Explanation of Solution
Given:
The mean diameter stays at
Calculation:
If the mean diameter stays at 3.98, then find the value of mean diameter that a supplier must set for the large-cup lids to ensure that less than 1% of the lids are too small to fit.
Solve for the appropriate standard deviation so that less than 1% of lids have diameter less than 3.95. First, find the z -value for which 1% of observations are lower. Using standard normal table, find the z value corresponding to
Hence, the proportion of observations less than 3.5 is approximately 1, so the proportion of observations greater than 3.5 is approximately 0. In other words, it is extremely rare for a lid to be too big.
Conclusion:
Therefore, it is extremely rare for a lid to be too big.
(c)
To find: whether option a or b is preferable.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 58E
Part (b) is preferred.
Explanation of Solution
Given:
The mean diameter stays at
Calculation:
Reducing the standard deviation is preferred. This will not increase the number of lids that are too big, but will reduce the number of lids that are too small. If the mean is shifted to the right, reduce the number of lids that are too small, but increase the number of lids that are too big.
Conclusion:
Therefore, part (b) is preferred.
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Elementary Statistics: Picturing the World (7th Edition)
Calculus: Early Transcendentals (2nd Edition)
Pre-Algebra Student Edition
Thinking Mathematically (6th Edition)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Algebra and Trigonometry (6th Edition)
- At the same restaurant as in Question 19 with the same normal distribution, what's the chance of it taking no more than 15 minutes to get service?arrow_forwardClint, obviously not in college, sleeps an average of 8 hours per night with a standard deviation of 15 minutes. What's the chance of him sleeping between 7.5 and 8.5 hours on any given night? 0-(7-0) 200 91109s and doiw $20 (8-0) mol 8520 slang $199 galbrog seam side pide & D (newid se od poyesvig as PELEO PER AFTE editiw noudab temand van Czarrow_forwardTimes to complete a statistics exam have a normal distribution with a mean of 40 minutes and standard deviation of 6 minutes. Deshawn's time comes in at the 90th percentile. What percentage of the students are still working on their exams when Deshawn leaves?arrow_forward
- Suppose that the weights of cereal boxes have a normal distribution with a mean of 20 ounces and standard deviation of half an ounce. A box that has a standard score of o weighs how much? syed by ilog ni 21arrow_forwardBob scores 80 on both his math exam (which has a mean of 70 and standard deviation of 10) and his English exam (which has a mean of 85 and standard deviation of 5). Find and interpret Bob's Z-scores on both exams to let him know which exam (if either) he did bet- ter on. Don't, however, let his parents know; let them think he's just as good at both subjects. algas 70) sering digarrow_forwardSue's math class exam has a mean of 70 with a standard deviation of 5. Her standard score is-2. What's her original exam score?arrow_forward
- Clint sleeps an average of 8 hours per night with a standard deviation of 15 minutes. What's the chance he will sleep less than 7.5 hours tonight? nut bow visarrow_forwardSuppose that your score on an exam is directly at the mean. What's your standard score?arrow_forwardOne state's annual rainfall has a normal dis- tribution with a mean of 100 inches and standard deviation of 25 inches. Suppose that corn grows best when the annual rainfall is between 100 and 150 inches. What's the chance of achieving this amount of rainfall? wved now of sociarrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
![Text book image](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)