The distribution of grade point averages (gpas) for medical school applicants of a certain year were approximately normal, with a mean of 3.48 and a standard deviation of 0.36. suppose a medical school will only consider candidates with gpas in the top 20% of the applicant pool. an applicant has a gpa of 3.75. does this gpa fall in the top 20% of the applicant pool?

So the score that separates the bottom 80% of data from the top 20% is 3.783. Since the value obtained by the applicant is 3.75 <3.783 not falls on the top 20%.  

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 grade point averages (GPAs) for medical school applicants of a certain year of a population, and for this case we know the distribution for X is given by:

Where and

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

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 in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. We can found this with the following excel code:"=NORM.INV(0.8,0,1)". On this case P(Z<0.842)=0.80 and P(Z>0.842)=0.2

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 score that separates the bottom 80% of data from the top 20% is 3.783. Since the value obtained by the applicant is 3.75 <3.783 not falls on the top 20%.  

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.