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Question

The mode of the binomial distribution for which mean and standard deviation are 10 and 5 respectively, is

A
7
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B
8
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C
9
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D
10
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Solution

The correct option is D 10
In a binomial distribution, mean, np=10 and variance, npq=5
[Since, variance=square of standard deviation]
10×q=5q=12
p=1q=112=12
Let x be the mode. Then,
np+q>x>npq
10+12>x>1012
212>x>1929.5<x<10.5
Hence, option (d) is correct.

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