Solve the Problems Below.

1.) Assume that the variable is normally distributed, the average time it takes a group of senior high school students to finish a certain examination is 40 minutes while the standard deviation is 5 minutes. (a.) What is the probability that a randomly selected senior high school students will complete the examination in less than 41 minutes? (b.) Does it seem reasonable that a senior high school student would finish the examination in less than 41 minutes?

(c.) If 55 randomly selected senior high school students take the examination, what is the probability that the mean time it takes the group to complete the test will be less than 41 minutes? (d.) Does it seem reasonable that the mean of the 50 senior high school students could be less than 41 minutes?

2. An electrical company claims that the average life of the bulbs it manufactures is 1 500 hours with a standard deviation of 300 hours. If a random sample of 150 bulbs is chosen, what is the probability that the sample mean will be between 1200 hours and 1 300 hours?