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 (integer)
96
Solution
Let two roots of a quadratic equation are mean = np and variance = npq.
<br/><br/>Given $n p+n p q=82.5$
<br/><br/>and $n p(n p q)=1350$
<br/><br/>$\therefore$ Quadratic equation is
<br/><br/>$ x^{2}-82.5 x+1350=0$
<br/><br/>$\Rightarrow x^{2}-22.5 x-60 x+1350=0$
<br/><br/>$\Rightarrow x-(x-22.5)-60(x-22.5)=0$
<br/><br/>Mean $=60$ and Variance $=22.5$
<br/><br/>$n p=60, n p q=22.5$
<br/><br/>$\Rightarrow q=\frac{9}{24}=\frac{3}{8}, p=\frac{5}{8}$
<br/><br/>$\therefore \quad n \frac{5}{8}=60 \quad \Rightarrow n=96$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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