The average hourly wage of workers at a fast-food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75? b) The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $97,750. For a female full professor at the same kind of institution, the salary is $90,280. If the standard deviation for the salaries of both genders is approximately $4700 and the salaries are normally distributed, find the 80th percentile salary for the male professors and for female professors, respectively.
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!
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