Question

1. a) The average score of golfers competing in the ACME INC Tournament is 71.5. In golf, the goal is to get the lowest score. A golfer knows he needs to be in the bottom 20% of scores in order to qualify for the next round of the tournament. If the standard deviation of the gold scores os 3.12 , he needs to score below what value in order to advance to the next round?

b) The average math SAT score for students applying to Brown university last year was 510 with a standard deviation of 89. What score does an applicant need to be in the top 1% of math sat scores?

Answer 1

Solution,

Given that,

a) mean = = 71.5

standard deviation = = 3.12

Using standard normal table

P(Z < z ) = 20%

P ( Z < z ) = 0.20

z = - 0.8416

Using z-score formula,

x = z * +

x = - 0.8416 * 3.12 + 71.5

x = 68.87

b) mean = = 510

standard deviation = = 89

Using standard normal table

P( Z > z) =1%

1 - P (Z < z) = 0.01

P ( Z < z ) = 1 - 0.01 = 0.99

P( Z < 2.326) = 0.99

z = 2.326

Using z-score formula,

x = z * +

x = 2.326 * 89 + 510

x = 717.01