A recent article in the Myrtle Beach Sun Times reported that the mean labor cost to repair a color television is $90 with a standard deviation of $22. Monte's TV Sales and Services completed repairs on two sets this morning. The labor cost for the first was $75 and it was $100 for the second. COmpute the values for each and comment on your finding.

You will need to "compute the values" yourself, but I see one thing to include in your comments: Both $75 and $100 are within the "standard deviation of $22." What do you think that means?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores.

Then you can comment.

To compute the values and provide comments on the findings, we need to calculate the z-scores for both repair costs using the formula:

z = (x - μ) / σ

Where:
z is the z-score,
x is the observed value,
μ is the mean, and
σ is the standard deviation.

1. For the first repair:
x = $75
μ = $90
σ = $22

Using the formula:
z1 = (75 - 90) / 22 ≈ -0.68

2. For the second repair:
x = $100
μ = $90
σ = $22

Using the formula:
z2 = (100 - 90) / 22 ≈ 0.45

Now, let's comment on the findings:

For the first repair with a labor cost of $75, the z-score is approximately -0.68. This means the labor cost is approximately 0.68 standard deviations below the mean. In other words, the cost for this repair is below average compared to the typical repair cost.

For the second repair with a labor cost of $100, the z-score is approximately 0.45. This means the labor cost is approximately 0.45 standard deviations above the mean. In other words, the cost for this repair is above average compared to the typical repair cost.

Therefore, based on the z-scores, we can conclude that the first repair had a below-average labor cost, while the second repair had an above-average labor cost compared to the mean labor cost of $90.