Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,225 per hour and a standard deviation of $220.
What is the operating cost for the lowest 5 percent of the airplanes?
According to the standard bell curve and the empirical rule, the lowest 5% would be 2 standard deviations below the mean making the operating cost of the lowest 5% of airplanes equal to $1785
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score related to that proportion.
For the lowest 5%, you need a Z score of -1.645.
Insert the values in the above equation to solve for the score.
.59
To find the operating cost for the lowest 5 percent of the airplanes, we need to determine the corresponding value in the normal distribution.
Step 1: Start by finding the z-score corresponding to the desired percentile. The percentile is given as 5 percent or 0.05.
Step 2: Use the z-score formula: z = (x - μ) / σ, where x is the value we want to find, μ is the mean, and σ is the standard deviation.
Step 3: Rearrange the formula to solve for x: x = z * σ + μ.
Step 4: Substitute the values into the formula:
z = -1.645 (the z-score corresponding to the 5th percentile, obtained from a standard normal distribution table)
μ = $2,225 (mean hourly cost)
σ = $220 (standard deviation)
x = -1.645 * $220 + $2,225
By substituting the values and calculating the expression, we can find the operating cost for the lowest 5 percent of the airplanes.
Note: Make sure to use the z-score corresponding to the desired percentile and the correct values for mean and standard deviation.
Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $5,018 per hour and a standard deviation of $493.
What is the operating cost for the lowest 1% of the airplanes? (Round z value to 2 decimal places and round final answer to nearest whole dollar.)
Operating cost