Using the appropriate normal transformation, what is the probability that the average salary of four randomly selected electricians is less than $50,000?
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!
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians’ yearly earnings is
Using the appropriate normal transformation, what is the
Let denotes the average salary. The given mean is $54,000 per year in the United States, and standard deviation is $12,000.
The probability that the average salary of four randomly selected electricians is less than $50,000 is,
The probability of z less than –0.6667 can be obtained using the excel formula “=NORM.S.DIST(–0.6667,TRUE)”. The probability value is 0.2525.
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