Question

at a photography contest, entries are scored on a scale from 1 to 100. at a recent contest with 1,000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. which of the following is the best description of the 77th percentile of the distribution?
a there were 770 entries with a score less than or equal to 68.
b there were at least 230 entries with a score of 77.
c there were 23% of the entries with a score less than or equal to 68.
d there were 77% of the entries with a score equal to 68.
e there were at least 77% of the entries with a score greater than 68.

Explanation:

Step1: Recall percentile definition

The $k$ - th percentile means $k$% of data is less than or equal to that value.

Step2: Calculate number of entries

For 77th percentile and 1000 entries, $0.77\times1000 = 770$. So 770 entries have score less than or equal to 68.

Answer:

A. There were 770 entries with a score less than or equal to 68.