published by SCC Inc, studied the income of engineers. They found the average yearly income after working 10 years was $186,000 dollars. The population standard deviation was $30,000.

i) Define the variable(s) you will use in your solution. [Defining variables]

Suppose you choose a single random income, and you compute the probability that the income is between $179,987 and $181,991. (ii) Write the result using proper probabiity notation and THEN write a complete sentence that describes your result in context. (Round to 4 decimal places.) Show your calculations OR a description of what StatCrunch menus/tools/commands and entries you used. Now suppose you take a random sample of size n=56n=56, and you compute the probability the sample has an average income between $179,987 and $181,991. (iii) Write the result using proper probability notation and THEN write a complete sentence that describes your result in contect. (Round to 4 decimal places.)Show your calculations OR a description of what StatCrunch menus/tools/commands and entries you used.