Question

For two Binomial random variables, one with p = 0.3 and the other with p = 0.7, which one would have the higher value at the 50th percentile of the associated distribution?

Neither, the Values Would be Equal

0.7

Need More Information

0.3

Answer 1

The answer is:

${\color{DarkRed} \text{Neither, the Values Would be Equal}}$

We will use graphs to compare the two binomial distributions

Let us consider a small sample of 10 records. Then for

i) p = 0.7

Binomial Graph 0.30000000 0.25000000 0.20000000 Probability P(X=x) 0.15000000 0.10000000 0.05000000 0.00000000 0 1 2 3 4 5 6 7 8 9 10

ii) p = 0.3

Binomial Graph 0.30000000 0.25000000 0.20000000 Probability P(X=x) 0.15000000 0.10000000 0.05000000 0.00000000 0 1 2 3 4 5 6 7 8 9 10

The 50th percentile value is the same for both p=0.7 and p=0.3.

This is because of 0.7+0.3=1

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