What percent of people have greater than 20 visits per year?

Question

You are working at the Behavioral Health Center in Kingsville, documenting the number of visits per year for each client. The mean is 16.5 visits per year and the standard deviation is 4.2.

Answer 1

Assuming the number of visits per year is normally distributed, mean 16.5, standard deviation 4.2.

x = number of visits

want to compute P(x > 20)

to find probability we convert to standard normal distribution, mean 0 standard deviation 1.

z = (x - mean)/standard deviation is normally distribution with mean 0 and standard deviation 1.

convert x from N(16.5,4.2) to z N(0,1):

P(z > (20-16.5)/4.2) = P( z > 0.833).

Since normal distribution is symmetric that is the same as P(z < -0.833) = 0.2033