In an environmental science class the test data goes as foll

Solution

Here N=30 , so using central limit theorem we can approximate normal distribution.

Using Normal approxiamation , find a score X\' whose probability is 0.85

P(X<=X\')=0.85, which is P(X>X\') =0.15, converting into standard normal values

P[Z>(X\'-Mean)/SD]=0.85

Here mean = 20; variance = 5.76 , standard deviation(SD) =sqrt(variance) =sqrt(5.76) = 2.4

From Normal tables P(Z>1.04)=0.15

Therefore X\'-Mean/SD = 1.04 , X\'= (1.04*2.4)+20 =22.496

The score should be 22.496 or more to be in the top 15%