Find Percentile

Question

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.6 days and a standard deviation of 2.4 days.

What is the 80th percentile for recovery times? (Round your answer to two decimal places.)

Answer 1

Hey there! To get this, we need to know the z score that is associated with the 80'th percentile is .8416. These can usually be found in the back of your textbook. A z score is basically asking, how many standard deviations away is this percentile? So, we take our SD of 2.4 and multiply by .8416 and we get 2.02. Then we add this to the mean, 5.6 and get 7.62!

Answer 2

One can (should?) also get the z-score for the 80th percentile using technology. On the TI-84:

1) Press [2nd]

2) Press [VARS]

3) in the DISTR menu, Select invNorm

4) Convert your percentile to decimal (80% = 0.80 here) and enter invNorm(0.80, 0, 1). Here the 0 and 1 are the mean and standard deviation for z-scores.

5) The result is 0.8416..., and from there you can follow Benjamin's method above.

You can also do this directly by entering invNorm(0.80, 5.6, 2.4) using the given mean of 5.6 and standard deviation of 2.4.