(3 points) Blades of grass Suppose that the heights of blades of grass are Normally distributed and independent, with each height having expected value 4 inches and standard deviation
0.75
inches. A child picks the blades of grass. (a) ( 1 point) What is the probability that the height of 1 blade of grass is 5 inches or taller? (b) (1 point) How many blades of grass does the child expect to pick until the first blade of grass appears with height 5 inches or taller? (c) (1 point) Now, instead of the setup in
1 b
, suppose that the child picks exactly 10 blades of grass. What is the expected number of blades of grass that have height 5 inches or taller, within this collection of 10 blades of grass?