**Problem 6: Analysis of Cylinder Diameter in Industrial Production**In an industrial operation at GEM Company, the diameter of a cylinder is a critical measurement. The buyer has specific requirements for this measurement: the diameter must be within 4.0 ± 0.02 cm. This means that any cylinder falling outside these specifications will be rejected.During the manufacturing process, it is observed that the diameter of a cylinder follows a normal distribution. The mean diameter is noted to be μ = 4.0 cm, with a standard deviation of σ = 0.013 cm.**Question:**On average, how many manufactured cylinders will be scrapped if they do not meet the diameter specifications set by the buyer?

Answered: Image /qna-images/answer/f2855507-d055-418d-b673-41a7c880f564.jpg

Answered: GEM Company: the diameter of a cylinder…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Everest auto industry produces bearing for Mahindra Motor Corporation. The precision of radius of bearing is very important for its successful functioning. To check the variability in the bearing radius, the company randomly selected ten bearings and measured the radius, the result of which is as shown in the table below. #no Nominal radius (cm) #no Nominal radius (cm) 1 2.70 6 2.59 2 2.65 7 2.73 3 2.75 8 2.64 4 2.55 9 2.88 5 2.76 10 2.83 Calculate the sample standard deviation for the above data. Construct a box plot and check whether there is any outlier data in the data distribution. Based on the comparison between the mean and the quartile, identify the shape of the data distribution. Calculate the 65th percentile and interpret the result. What is the range of the data distribution? Explain its meaning.
1. Draw by hand or in Excel fully labelled curves on a common scale to represent two sets of scores where:a.Mean = 25, Standard Deviation = 4,Mean = 50, Standard Deviation = 4.b.Mean = 50, Standard Deviation = 2,Mean = 50, Standard Deviation = 5.
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A variable is normally distributed with mean 17 and standard deviation 8. Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed. a) Find the area to the left of 16. b) Find the area to the left of 13. c) Find the area to the right of 15. d) Find the area to the right of 19. e) Find the area between 13 and 28.
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A variable is normally distributed with mean 34 and standard deviation 11. Use the Cumulative Z-Score Table to answer the following questions. Write your answers in decimal form using 4 decimal places. a) Find the area under the normal curve to the left of the data value 63.7. b) Find the area under the normal curve to the left of the data value 2.1. c) Find the area under the normal curve to the right of the data value 30.7. d) Find the area under the normal curve to the right of the date value 29.05. e) Find the area under the normal curve between the data values 2.1 and 29.05.
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1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. a. Draw the density curve for the normal distribution of pregnancy lengths. Mark and label the location the mean and three standard deviations above and below the mean. b. Answer the following questions using the density curve you drew for part a. It may help to shade relevant parts of the curve. i. What percent of the pregnancies last between 250 and 282 days? ii. What are the upper and lower bounds for the middle 95% of all pregnancy lengths? iii. What percent of the pregnancies last between 218 and 314 days? iv. What percent of the pregnancies last 266 days or fewer? v. What percent of the pregnancies last between 266 and 282 days? vi. What percent of the pregnancies last fewer than 250 days? vii. What percent of the pregnancies last between 234 and 314 days? viii. How long are the longest 2.5% of…
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