Agnes Hammer is a senior majoring in management science. She has been interviewing with several companies for a job when she graduates, and she is curious about what starting salary offers she might receive. There are 140 seniors in the graduating class for her major, and more than half have received job offers. She asked 12 of her classmates at random what their annual starting salary offers were, and she received the following responses:
$28,500 ..... $35,500
32,600 ..... 36,000
34,000 .... 25,700
27,500 .... 29,000
24,600 ...... 31,500
34,500 ...... 26,800
Assume that starting salaries are normally distributed. Compute the mean and standard deviation for these data and determine the probability that Agnes will receive a salary offer of less than $27,000.