A section of highway is posted with a 55 mph speed limit. In fact, speeds of cars traveling on this section are normally distributed with mean 58 mph and standard deviation 5 mph. If the state patrol decides to ticket cars in the fastest 10 %, at what speed will they start ticketing

And if we solve for a we got

So the value of height that separates the bottom 90% of data from the top 10% is 64.4.  

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 velocity of a population, and for this case we know the distribution for X is given by:

Where and

For this part we want to find a value a, such that we satisfy this condition:

  (a)

  (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

But we know which value of z satisfy the previous equation so then we can do this:

And if we solve for a we got

So the value of height that separates the bottom 90% of data from the top 10% is 64.4.  

on december 1, 1774, the continental association was created to boycott all contact with british goods. by reversing the economic sanctions placed on the colonists, the delegates hoped britain would repeal its intolerable acts.

aren't cheetos good enough to be president?