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.
