Under a normal distribution curve, if 70% of the people fall to the right of the observation point, then 30% of the people would fall to the left of the observation point. Note, the observation point is the number we are looking for in this instance(how long it takes to find a parking space).
We'll need to use a z table and the formula for a z score to find what we are looking for. First, convert 30% to 0.30 and refer to a standard z table that represents the area under a normal curve to the left of specific z scores. We'll need to look in the body of the table and find the closest decimal value compared to our 0.30. Once you find this decimal number, reference the row and column values to obtain the z score. Looks like this will be -0.53.
Now we can use the z score formula to find our observation point:
z score = (x - Mean)/standard deviation, where x represents the observation point we're looking for!
Substituting into the formula we have: [tex]-0,53 = \frac{x-4}{2} [/tex]
Solving this equation for x, we find x = 2.94
This represents our observation point and we can assume that 70% of people take more than 2.94 minutes to find a parking space.
