The length of time it takes to find a parking space at 9 A. M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. Seventy percent of the time, it takes more than how many minutes to find a parking space? (Round your answer to two decimal places.)

And if we solve for a we got

Step-by-step explanation:

Let X the random variable that represent the lenght time it takes to find a parking space at 9AM 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)

As we can see on the figure attached the z value that satisfy the condition with 0.7 of the area on the left and 0.3 of the area on the right it's z=0.524

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

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.