In an environmental science class, the test data goes as follows - N - 30 Mean -

Question

In an environmental science class, the test data goes as follows -
N - 30 Mean - 20 Median - 22 Mode - 24 Standard deviation - (blank) Variance - 5.76 Highest score - 30 Lowest score - 18 Range - 12
What score would you need to be in the top 15%?
In an environmental science class, the test data goes as follows -
N - 30 Mean - 20 Median - 22 Mode - 24 Standard deviation - (blank) Variance - 5.76 Highest score - 30 Lowest score - 18 Range - 12
What score would you need to be in the top 15%?

N - 30 Mean - 20 Median - 22 Mode - 24 Standard deviation - (blank) Variance - 5.76 Highest score - 30 Lowest score - 18 Range - 12
What score would you need to be in the top 15%?

Explanation / Answer

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%

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