Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,175 per hour and a standard deviation of $175.
What is the operating cost for the lowest 10 percent of the airplanes? (Round z value to 2 decimal places. Omit the "$" sign in your response.)
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 (.10) and its Z score.
Insert all data in above equation.
To find the operating cost for the lowest 10 percent of the airplanes, you would need to find the corresponding z-score and then use it to calculate the actual cost.
1. First, let's find the z-score corresponding to the lowest 10 percent. The z-score represents the number of standard deviations a given value is from the mean in a normal distribution. We will use the standard normal distribution table (also known as the Z-table) to find this value.
The z-score for the lowest 10 percent corresponds to a cumulative probability of 0.10. Looking up this value in the Z-table, we find that the closest z-score is approximately -1.28.
2. Now that we have the z-score (-1.28), we can use it to calculate the actual operating cost. The formula to convert a z-score to an actual value is:
Z = (X - μ) / σ
Where:
Z is the z-score,
X is the actual value,
μ is the mean, and
σ is the standard deviation.
We want to find X, so we rearrange the formula:
X = Z * σ + μ
Plugging in the values:
Z = -1.28
σ = $175 (standard deviation)
μ = $2,175 (mean)
X = -1.28 * $175 + $2,175
3. Finally, we can calculate the operating cost for the lowest 10 percent of the airplanes:
X = -$224 + $2,175
X = $1,951
Therefore, the operating cost for the lowest 10 percent of the airplanes is approximately $1,951.