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?

Answer 1

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 %