A. A manufacturer knows that their items have a normally distributed length, with a mean of 12.6 inches and a standard deviation of 4.1 inches. If 18 items are chosen at random, what is the probability that their mean length is less than 13.9 inches? Enter your answers as numbers accurate to 4 decimal places.
B. On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 368 pounds and a standard deviation of 53 pounds. The cow transport truck holds 11 cows and can hold a maximum weight of 4246 pounds. If 11 cows are randomly selected from the very large herd to go on the truck, what is the probability that their total weight will be over the maximum allowed of 4246 pounds?
C. A population of values has a normal distribution with μ=130.9 and σ=71.3. You intend to draw a random sample of size n=81. Please answer the following questions and show your answers to 1 decimal place.
- Find the value separating the bottom 19% values from the top 81% values.
- Find the sample mean separating the bottom 19% sample means from the top 81% sample means.
D. Based on historical data, your manager believes that 43% of the company's orders come from first-time customers. A random sample of 175 orders will be used to estimate the proportion of first-time customers. What is the probability that the sample proportion is between 0.28 and 0.44?
E. In a recent year, the Better Business Bureau settled 75% of complaints they received. You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Suppose your sample size is 109. What is the probability that the sample proportion will be at least 5 percent more than the population proportion? (4 decimal places)