Smalltown elevator produces elevator rails. To meet specifications, an elevator rail must be between 0.995 inches and 1.005 inches in diameter. Suppose that the diameter of an elevator rail follows a normal random variable with mean of 1 inch and standard deviation of 0.003 inches. Rounded to the nearest one tenth of one percent, what fraction of all elevator rails will meet specifications?
Answers
Answer:
90.5 %
Step-by-step explanation:
Smalltown elevator produces elevator rails. To meet specifications, an elevator rail must be between 0.995 inches and 1.005 inches in diameter. Suppose that the diameter of an elevator rail follows a normal random variable with mean of 1 inch and standard deviation of 0.003 inches. Rounded to the nearest one tenth of one percent, what fraction of all elevator rails will meet specifications?
z = ( x - mean)/standard deviation
z = (0.995 -1)/(0.003)
z = - 0.005/0.003
z = - 5/3
z = -1.67
z = (1.005 -1)/0.003
z = 1.67
% between z score -1.67 & 1.67 will meet specifications.
4.75 % below -1.67
95.25 % below 1.67
between -1.67 & 1.67 = 95.25 - 4.75 = 90.5 %
905/1000 = 181/200 fraction of all elevator rails will meet specifications
