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 $p$ -th percentile of a data - set is a value such that $p$ percent of the data values are less than or equal to that value. Here, the 77th percentile score is 68. This means that 77% of the 1000 entries have a score less than or equal to 68.

Step2: Calculate number of entries

The number of entries with a score less than or equal to 68 is $0.77\times1000 = 770$.

Answer:

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