JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Probability

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The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is:

Answer: 96

Solution

Let mean

m = n p

and variance

v = n pq

where

p + q = 1

. Given

m + v = 82.5

and

m v = 1350

. These are roots of

t^{2} - 82.5 t + 1350 = 0

, giving

t = 60

t = 22.5

. So

m = 60

and

v = 22.5

. From

v = n pq

and

m = n p

, we have

q = \frac{v}{m} = \frac{22.5}{60} = \frac{3}{8}

, so

p = \frac{5}{8}

. Thus

n = \frac{m}{p} = \frac{60}{5/8} = 96

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Integer answer

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