Question

To qualify for a Master’s degree program in Business Administration at Stanford University, candidates must score in the top 10% on a mental ability test. The test has a mean of 190 and a standard deviation of 25. Find the lowest possible score to qualify. Assume the test scores are normally distributed.

Step 1: Draw a figure and represent the area.

Step 2: Find the z value.

Step 3: Answer the question. 

Answer 1

1.

2.

$$P(Z>z)=1-P(Z\leq z)=1-0.1$$

$$P(Z\leq z)=0.1$$

$$z\approx1.28155$$

3.

$$z=\dfrac{x-190}{25}=1.28155$$

$$x=190+1.28155(25)$$

$$x=222.03875$$

The lowest possible score to qualify is 222.