Question

The mean salary at a local industrial plant is $26,500 with a standard deviation of $5000. The median salary is $27,200 and the 57th percentile is $30,400. Based on the given information, determine if the following statements are true or false.

a. Approximately 7% of the salaries are between $26,500 and $30,400.
b. The percentile rank of $25,400 is 50.

Answer 1

Approximately 7% of the salaries are between $26,500 and $30,400. The percentile rank of $25,400 is less than 50.

Step-by-step explanation:

To determine if the statements are true or false, we need to analyze the given information.

a. The statement is true. The mean salary is $26,500 and the 57th percentile is $30,400. Since the mean is lower than the 57th percentile, approximately 50% of the salaries are below $26,500 and approximately 7% are between $26,500 and $30,400.

b. The statement is false. The median salary is $27,200, which means that 50% of the salaries are below $27,200. Therefore, the percentile rank of $25,400 would be less than 50.