Answer to Question 1 in Comparison of Means

Question

At a board meeting,  you hear different statements about who the clinic is serving.  According to the statements, 68% of the patients are under 25 years old and 10% are over 50 years old. Assuming that the patients are normally distributed, find the mean and standard deviation of the distribution.     z Online Calculator►

Answer

To solve this problem, first find out the standard Z-value  associated with 25 and 50. The equation for calculating the z critical value is given as:

Looking up z values in an online calculator.  Note that 68% of the data are below a z-value of 0.4678.  This provides us with the following equation:

A similar calculation can be done for the situation where 10% of patients are above 50 years. Solve the two equations to find the average and standard deviation.