Final answer:
The shrinkage in length of a certain brand of blue jeans is normally distributed with a mean of 1.1 inches and a standard deviation of 0.2 inch. To find the percent of jeans that will shrink more than 1.4 inches, we use the cumulative distribution function (CDF). To find the percent of jeans that will shrink between 0.8 and 1.45 inches, we subtract the cumulative probability at 0.8 inches from the cumulative probability at 1.45 inches.
Step-by-step explanation:
The shrinkage in length of the blue jeans is normally distributed with a mean of 1.1 inches and a standard deviation of 0.2 inch. To find the percent of jeans that will shrink more than 1.4 inches, we need to calculate the area under the normal curve to the right of 1.4 inches. We can use the cumulative distribution function (CDF) to find this probability. Using a calculator or a standard normal table, we find that the probability is approximately 0.1056, which is equivalant to 10.56%.
To find the percent of jeans that will shrink between 0.8 and 1.45 inches, we need to calculate the area under the normal curve between 0.8 and 1.45 inches. We can subtract the cumulative probability at 0.8 inches from the cumulative probability at 1.45 inches to find this probability. Using a calculator or a standard normal table, we find that the probability is approximately 0.4664, which is equivalent to 46.64%.