Example 97

Example 97:   In 2011, the highest starting salaries for recent college graduates were paid to chemical engineering majors.  The average starting salary for chemical engineers in 2011 was $66,886, and the standard deviation was $7,500.  The distribution of starting salaries for chemical engineers appears to be normal.  Find the following probabilities:

a) Find the probability that one randomly selected chemical engineer receives a starting salary less than $58,000.

b) Find the probability of 36 randomly selected chemical engineers having an average starting salary less than $58,000.