Question
The lengths of what are considered "1 inch bolts are found to be normally distrubted with a mean of 1.001 inches and a standard deviation of 0.002 inches. If a bolt measures more than 2 standard deviations away from the mean, it is rejected for not meeting factory tolerances.
a. what are the minimum and maximum lengths required for a bolt to meet factory tolerances?
b. what percentage of bolts will be rejected?
a. what are the minimum and maximum lengths required for a bolt to meet factory tolerances?
b. what percentage of bolts will be rejected?
Answers
bobpursley
You need to memorize this, pronto.
In addition to being more understandable than the variance as a measure of the amount of variation in the data, the standard deviation summarizes how close observations are to the mean in a very nice way. Many variables in biology fit the normal probability distribution fairly well. If a variable fits the normal distribution, 68.3 percent (or roughly two-thirds) of the values are within one standard deviation of the mean, 95.4 percent are within two standard deviations of the mean, and 99.7 (or almost all) are within 3 standard deviations of the mean.
within 1 standard deviation: 68.3 %
within 2 standard deviations: 95.3 %
within 3 standard deviations: 99.7 %
In addition to being more understandable than the variance as a measure of the amount of variation in the data, the standard deviation summarizes how close observations are to the mean in a very nice way. Many variables in biology fit the normal probability distribution fairly well. If a variable fits the normal distribution, 68.3 percent (or roughly two-thirds) of the values are within one standard deviation of the mean, 95.4 percent are within two standard deviations of the mean, and 99.7 (or almost all) are within 3 standard deviations of the mean.
within 1 standard deviation: 68.3 %
within 2 standard deviations: 95.3 %
within 3 standard deviations: 99.7 %