The lengths of lumber a machine cuts are normally distributed with a mean of 104 inches and a standard deviation of 0.4 inch. a) What is the probability that a randomly selected board cut by the machine has a length greater than 104.17 inches? b) A sample of 42 boards is randomly selected. What is the probability that their mean length is greater than 104.17 inches? a) The probability is. Round to four decimal places as needed.)

Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.   The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.90 years and a standard deviation of 1.80 years. Random samples of size 20 are drawn from the population and the mean of each sample is determined. Round the answers to the nearest hundredth.       Answer choices:  A.) 5.90 years , 0.40 years b) 5.90 years , 0.09 years c.) 1.32 years , 1.80 years d) 1.32 years , 0.40 years

Given that we have a normal distribution with mean 73 and standard deviation of 13 for an English class's performance. What is the probability of getting a score of 86 or better? A) 0.1587 B) 0.8413 C) 0.3413 D) 0.0013

The average price of a college math textbook is $169 and the standard deviation is $25. Suppose that 49 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a.) What is the distribution of ¯x? ¯x ~ N(__,__) b.) For the group of 49, find the probability that the average price is between $172 and $176. c.) Find the 95th percentile for the average textbook price for this sample size. $___. Round to the nearest cent. d.) Find the 95th percentile for an individual textbook price. (round to the nearest cent) $___ e.)For part b), is the assumption that the distribution is normal necessary? YesNo