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 normally distributed and that the standard deviation is σ = $12,000. what is the probability that the average salary of four randomly selected electricians is less than $50,000?

The probability that the average salary of four randomly selected electricians is less than $50,000 is 25.25%.

Since the question gives us the population mean, population standard deviation, sample size (four) and the point estimate, we need to use the formula :

Z = [(X-μ)/(σ/√n)]

in order to arrive at the value of Z.

By substituting the values, we get

Z = (50,000 - 54000)/(12000/√4)

Z = -4000/6000

Z = - 0.666667

Once we have, we can use Z tables or an online calculator to look up the area under the standard normal curve below Z = -0.66667 (area to the left of Z = -0.66667). This gives us 0.2525 and this is expressed as a percentage for the answer.

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