Discuss the below:
Q1) The population of lengths of aluminum-coated steel sheets is normal distributed with a mean of 30.05 inches and a standard deviation of 0.3 inches. What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 inches long?
Q2) In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of 0.3 inches. What is the 95% confidence interval for the true mean length of the bolt?
Q3) The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue) For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company?