Heights of 10 year olds, Part III

Heights of \({{ params.age }}\) year olds, regardless of gender, closely follow a normal distribution with mean \({{ params.mean }}\) inches and standard deviation \({{ params.std }}\) inches.

Part 1

What fraction of \({{ params.age }}\) year olds are taller than \({{ params.height }}\) inches?

Part 2

If there are \({{ params.size }}\) \({{ params.age }}\) year olds entering Six Flags Magic Mountain in a single day, then compute the expected number of \({{ params.age }}\) year olds who are at least \({{ params.height }}\) inches tall. (You may assume the heights of the 10-year olds are independent.)

Part 3

Using the binomial distribution, compute the probability that \({{ params.number }}\) of the \({{ params.size }}\) \({{ params.age }}\) year olds will be at least \({{ params.height }}\) inches tall.

Part 4

The number of \({{ params.age }}\) year olds who enter Six Flags Magic Mountain and are at least \({{ params.height}}\) inches tall in a given day follows a Poisson distribution with mean equal to the value found in part (2). Use the Poisson distribution to identify the probability no \({{ params.age }}\) year old will enter the park who is \({{ params.height }}\) inches or taller.

Attribution

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.