Wait times at an orthodontist's office are typically 17 minutes, with a standard deviation of 2 minutes. what percentage of people should be seen by the doctor between 11 and 23 minutes for this to be considered a normal distribution?

The percentage is 99.73%

Step-by-step explanation:

* Lets explain how to solve the problem

- The wait times at an orthodontist's office are typically 17 minutes,

  with a standard deviation of 2 minutes

∴ μ = 17 and σ = 2

- To find the percentage of people should be seen by the doctor

  between 11 and 23 minutes for this to be considered a normal

  distribution we should to calculate the z-score between 11 and 23

∵ The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

∵ x = 11 , 23

∵ μ = 17 and σ = 2

∴ z = (11 - 17)/2 = -6/2 = -3

∵ z = (23 - 17)/2 = 6/2 = 3

- Use the table of z to find the percentage of -3 , 3

∵ P(z > -3) = 0.135%

∵ P(z < 3) = 99.865%

∴ P(-3 < z < 3) = 99.865 - 0.135 = 99.73%

∵ P(11 < x < 23) = P(-3 < z < 3)

∴ P(11 < x < 23) = 99.73%

* The percentage is 99.73%