What is the 75th percentile of the adhesion distribution?
A locomotive's 'adhesion' is the locomotive's pulling force as a multiple of its weight. A diesel locomotive model has adhesion which varies in actual use according to a Normal distribution with a mean .037 and a variance of 0.0016.
Can someone tell me how to do this problem thanks
To find the 75th percentile of the adhesion distribution, you need to follow these steps:
1. Convert the given information about the adhesion distribution to the standard normal distribution by calculating the z-score.
The z-score formula is: z = (x - μ) / σ
where:
- x is the value in question (75th percentile)
- μ is the mean of the distribution (0.037)
- σ is the standard deviation of the distribution (square root of variance, which is √0.0016)
2. Look up the z-score in the standard normal distribution table or use a statistical calculator to find the corresponding percentile.
The standard normal distribution table provides the area under the curve up to a specific z-score. The percentile is the area to the left of the z-score.
3. Calculate the corresponding percentile from the z-score.
For instance, if the z-score corresponds to a percentile of 0.75, it means that 75% of the data falls below the given value.
4. Convert the percentile back to the adhesion scale.
Using the inverse of the z-score formula: x = μ + z * σ
Substitute the found percentile value (as a z-score) into the equation to get the adhesion value at the 75th percentile.
By following these steps, you will be able to determine the 75th percentile of the adhesion distribution.