The Director of Analytics Salaries in the United States is estimated from a large group of employees, users, and past and present job advertisements on a large job search platform in the past 36 months. Based on the survey, Let us assume the parameters are as follows:

Average salary = = $146,589 per year Standard deviation = = $20,000

Amazonwants to study a sample of 30 Directors of Analytics; they need your short analytical summary for planning.(Assume the bonus and benefits are industry standard. Assume the Salary paid corresponds to the skill percentile position of the candidate.)

1.What is the probability the sample mean will exceed $146,589, what is your inference?

2.What is the probability the sample mean will exceed $155,000, what is your inference?

3.What is the probability the sample mean will exceed $175,000, what is your inference?