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 exceeds $60,000?Multiple Choice0.15870.69150.30850.8413

To solve this problem, we need to use the concept of the Central Limit Theorem which states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the shape of the population distribution.

Here are the steps to solve this problem:

1. First, we need to find the mean (µ) and the standard deviation (σ) of the population. From the problem, we know that µ = $54,000 and σ =$12,000.

2. Next, we need to find the mean and standard deviation of the sample distribution. The mean of the sample distribution is the same as the mean of the population, so µ_sample = $54,000. The standard deviation of the sample distribution is the standard deviation of the population divided by the square root of the sample size (n). So, σ_sample = σ / sqrt(n) =$12,000 / sqrt(4) = $6,000.

3. Now, we need to find the z-score for $60,000. The z-score is the number of standard deviations a particular score is from the mean. We can find the z-score using the formula: z = (X - µ_sample) / σ_sample = ($60,000 - $54,000) /$6,000 = 1.

4. Finally, we need to find the probability that the z-score is greater than 1. We can find this by looking up the z-score in a standard normal distribution table or using a calculator. The area to the left of z = 1 is 0.8413, so the area to the right (which is the probability we're looking for) is 1 - 0.8413 = 0.1587.

So, the probability that the average salary of four randomly selected electricians exceeds $60,000 is 0.1587. Therefore, the answer is 0.1587.