(Please show all work)
1. The time required to complete a project is known to be normally distributed with a mean of 46 weeks and a standard deviation of 4 weeks.
(a) What is the probability that the project is finished in 40 weeks or less?
(b) What is the probability that the project is finished in 52 weeks or less?
(c) There is an 80 percent chance that the project will be finished in less than how many weeks?
2. An urn contains 7 blue and 3 yellow chips. If the drawing of two chips in succession is done with replacement, determine the probability of:
(a) drawing a blue chip on the first draw and a yellow chip on the second draw
(b) drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw
(c) drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw
(d) drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw