Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.

(a) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What percent of 10 year olds cannot go on this ride?

(b) Suppose there are four 10 year olds. What is the chance that at least two of them will be able to ride Batman the Ride?

(c) Suppose you work at the park to help them better understand their customers' demographics, and you are counting people as they enter the park. What is the chance that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park?

(d) What is the chance that the fifth 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park?