![emileep13](/avatars/4874.jpg)
emileep13
06.07.2021 •
Mathematics
Precision manufacturing: A process manufactures ball bearings with diameters that are normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter. Round the answers to at least four decimal places. (a) Find the 60th percentile of the diameters. (b) Find the 67th percentile of the diameters. (c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be
Solved
Show answers
More tips
- F Food and Cooking How to Get Reconfirmation of Registration?...
- C Computers and Internet How to Get Rid of Spam in ICQ?...
- A Art and Culture Who Said The Less We Love a Woman, the More She Likes Us ?...
- F Family and Home How to Get Rid of Your Neighbors?...
- S Society and Politics How Could Nobody Know About the Dead Mountaineers?...
- H Health and Medicine How to Cure Adenoids?...
- H Health and Medicine Why Wearing a Back Brace Can Be Beneficial During Back Strain?...
- S Sport When and Where Will the 2014 World Cup be Held?...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
Answers on questions: Mathematics
- M Mathematics Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [Start 2 By 3 Matrix 1st Row 1st Column 1 2nd Column 4 3rd Column negative...
- M Mathematics A zookeeper published the following stem-and-leaf plot showing the number of bears at each major zoo in the country: How many zoos have exactly 16 bears?...
- M Mathematics Find the solution of the differential equation that satisfies the given initial condition....
- M Mathematics 34:14 What is the length of line segment KJ? O 2v3 units O 32 units O 3v3 units O 35 units...
- M Mathematics Which input value produces the same output value for the two functions? g(x) The tables represent the functions f(x) and g(x). х f(x) Х -3 -5 -3 -13 -2 -3 -2. -9 -1 -1 -1 -5 0 0...
- M Mathematics Please help me this is my last question please...
- M Mathematics A red bird is flying at an elevation of 17 1/9 meters. A blue bird was flying at an elevation of 10 3/5...
- M Mathematics Simplify the expression by combining like terms. 22+5−4+7−8...
- M Mathematics PLEASE HELP ME THANKS :( By decreasing each dimension by 3 units, the area of a rectangle decreased from 60 square feet to 18 square feet. Find the percent decrease in area....
- M Mathematics Which of the following is not true if the polygon is a square? O A. slopers. slopesc = -1, slope slopesc = -1, sloped slope = -1, and slope AB • Slopezd = -1 B. The slopes of the...
Ответ:
a) The 60th percentile of the diameters is of 25.0177 millimeters.
b) The 67th percentile of the diameters is of 25.0308 millimeters.
c) The diameter of the hole should be of 24.8562 millimeters.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter.
This means that![\mu = 25, \sigma = 0.07](/tpl/images/1390/0342/fb58c.png)
(a) Find the 60th percentile of the diameters.
This is X when Z has a p-value of 0.6, so X when Z = 0.253.
The 60th percentile of the diameters is of 25.0177 millimeters.
(b) Find the 67th percentile of the diameters.
This is X when Z has a p-value of 0.67, so X when Z = 0.44.
The 67th percentile of the diameters is of 25.0308 millimeters.
(c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be.
This is the 2nd percentile, which is X when Z has a p-value of 0.08, so X when Z = -2.054.
The diameter of the hole should be of 24.8562 millimeters.
Ответ: