Question

A survery of New York Dentists shows the cost of a certain dental procedure is normally distributed with a mean cost of $350 and a standard deviation of $40. Be sure convert your analysis from dollars to z-scores. ( Answer the following probability quesitons using Excel and show your work.

A, Draw a Picture( by hand) of the probability density function and mark the x axis in dollars with values from 1,2, and 3 standard deviations above and below the mean.

b. If you pick a dentist at random, What is the probability this procedure will cost less than $300?

C. What is the probability the cost will be greater than $400? ( Are you surprised between your answers to b and C?

D. What is the Probability the cost will be between $310 and $410?

E. One Dentist claims he is cheaper than 95% of all dentist in New York. What would he charge for this procedure if he is telling the truth?

F. what range of cost would be considered outliers?

Answer 1

Let X is a random variable shows the cost of dental procedure. Here X has normal distribution with parameter as follows:

A:

Folloiwng is the curve:

b)

The z-score for X = 300 is

The  probability this procedure will cost less than $300 is

(C)

The z-score for X = 400 is

The  probability this procedure will cost less than $300 is

D:

The z-score for X = 310 is

The z-score for X = 410 is

The probability the cost will be between $310 and $410 is

E:

Here we need z-score that has 0.95 area to it right and 0.05 area to its left. The z-score -1.645 has 0.05 area to its left. The required cost is

Answer: $284.20

F:

For standard normal distribution values that are above and below 2 standard deviations of mean are considered as outliers.

That is required range is: