Answer:
Standard deviation = 11.30 m/h
Mean = 57.74 m/h
Step-by-step explanation:
Assume that the travel speed is normally distributed.
The corresponding z-score to the 5th and 90th percentile of normal distribution are, respectively, -1.645 and 1.282.
For any given speed X, the z-score is:
[tex]z= \frac{X-\mu}{\sigma}[/tex]
If z = -1.645 for X = 39.15 and z= 1.282 for X=72.23, the following system can be solved for the mean and standard deviation of vehicle speed:
[tex]-1.645= \frac{39.15-\mu}{\sigma}\\1.282= \frac{72.23-\mu}{\sigma}\\\\-1.645 -1.282 = \frac{39.15-72.23}{\sigma} \\\sigma=11.30\ m/h\\\mu =72.23-(1.282*\sigma)\\\mu=57.74\ m/h[/tex]
The standard deviation is 11.30 m/h and the mean is 57.74 m/h.
