Question 718:

Asked on May 5, 2009

Tags: Z-Score

1

Answer:

No answer provided yet.We need to use the formula for a z-score to figure out what the minimum score at Lamar High School is and whether these students will make the cut. The formula is (data-point-mean)/standard deviation =z-score.  First we will find the z-scores for each student.

Bill:

1. (87-85)/5 = .4
2. We need to lookup the 1-sided area for a z-score of .4 using a normal table or the excel function = NORMSDIST(.4) and we get the area of .6554. meaning bill is in the 65.5th percentile--so he doesn't make the cut.

Mary

1. (95-85)/5 = 2.2
   
2. We need to lookup the 1-sided area for a z-score of 2.2 using a normal table or the excel function = NORMSDIST(2.2) and we get the area of .9861. meaning Mary  is in the 98.61th percentile--so she DOES make the cut.

To find the minimum score needed to make the cut we need to 1st find the z-score for the top 10%. We can use the excel function = NORMSINV(.90) and we get 1.28152.  Now we plug this into the z-score equation and use a little bit of algebra to isolate the unknown minimum score.

1. (min score - 85)/5 = 1.28152
   
2. (min score - 85) = 6.407758
3. min score = 91.40776

So you need at least a 91.41 score to be in the top 10% of Lamar High and make the cutoff to get into the UT schools.