1. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.7 years, and standard deviation of 1.8 years. If you randomly purchase 4 items, what is the probability that their mean life will be longer than 10 years? Round your answer to four decimal places.

2. A population of values has a normal distribution with =244.2 and =32.1. You intend to draw a random sample of size n=180. Find the probability that a sample of size n=180 is randomly selected with a mean between 245.9 and 248.5. P(245.9 < M < 248.5) = Enter your answers as numbers accurate to 4 decimal places.

3. In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.7 inches, and standard deviation of 5.1 inches. What is the probability that the height of a randomly chosen child is between 40.95 and 43.35 inches? (Round your answer to 4 decimal places.)