What waiting time represents the 90th ​percentile?

Question

The time spent (in days) waiting for a kidney transplant for people ages 35-49 can be approximiated by the normal distribution, as shown in the figure to the right.

Answer 1

This question cannot be answered without the table. However, if we want the 90% percentile, this means the remaining 10% of the population occurs to the right of this score and 90% of the population lies below this value. Therefore, the z-value corresponding to this score must be such that when we compare the z-value to the z-table, we get 0.90 (the 90% of people who scored lower than this value). Look at the z-table and see the z-value which corresponds t0 90% (0.90) on the left is 1.28. But we know how to calculate a z-value!

 

z= (x-mean)/standard deviation 

 

So we want a value x such that 

 

1.28 = (x-mean)/standard deviation

 

Just use the information you are given and solve for x.