Vehicle speed on a particular bridge in China can be modeled as normally distributed. (a) If 5% of all vehicles travel less than 39.18 m/h and 10% travel more than 73.23 m/h, what are the mean and standard deviation of vehicle speed?

  (1)

  (2)

From equation (1) and (2) we can solve for and we got:

  (3)

  (4)

And we can set equal equations (3) and (4) and we got:

And solving for the deviation we got:

And the mean would be:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the vehicle speed of a population, and for this case we know the distribution for X is given by:

For this case we know the following conditions:

And the best way to solve this problem is using the normal standard distribution and the z score given by:

We look for a one z value that accumulate 0.05 of the area in the left tail and we got: and we need another z score that accumulates 0.1 of the area on the right tail and we got

And we have the following equations:

  (1)

  (2)

From equation (1) and (2) we can solve for and we got:

  (3)

  (4)

And we can set equal equations (3) and (4) and we got:

And solving for the deviation we got:

And the mean would be: