According to the job search website Indeed, the average starting salary for teachers for new college graduates in education is $59,025. The average starting salary for financial analysts for new college graduates in finance is $63,544 (report on “How much Canadians earn according to their university major” at http://dailyhive.com/vancouver/canadians-university-major-salary-indeed-2017, August 10, 2017). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for teachers for new college graduates in education is $8,000. Assume that the standard deviation for starting salaries for financial analysts for new college graduates in finance is $9,000. (2) What is the probability that a new college graduate in education will earn a teacher starting salary less than $50,000? Hint: Use Excel function NORM.DIST. (2) What is the probability that a new college graduate in education will earn a teacher starting salary of at least $70,000? (2) What is the probability that a new college graduate in finance will earn a starting financial analyst salary of at least $70,000? (3) How much would a new college graduate in finance have to earn as a financial analyst in order to have a starting salary higher than 99% of all starting teacher salaries of new college graduates in education?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
According to the job search website Indeed, the average starting salary for teachers for new college graduates in education is $59,025. The average starting salary for financial analysts for new college graduates in finance is $63,544 (report on “How much Canadians earn according to their university major” at http://dailyhive.com/vancouver/canadians-university-major-salary-indeed-2017, August 10, 2017). Assume that starting salaries are
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(2) What is the probability that a new college graduate in education will earn a teacher starting salary less than $50,000?
Hint: Use Excel
function NORM.DIST. -
(2) What is the probability that a new college graduate in education will earn a teacher starting salary of at least $70,000?
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(2) What is the probability that a new college graduate in finance will earn a starting financial analyst salary of at least $70,000?
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(3) How much would a new college graduate in finance have to earn as a financial analyst in order to have a starting salary higher than 99% of all starting teacher salaries of new college graduates in education?
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