Statistics And Probability Question 506
Question: The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution is
[MP PET 2002]
Options:
A) $ {}^{16}C_6{{( \frac{1}{4} )}^{10}}{{( \frac{3}{4} )}^{6}} $
B) $ {}^{16}C_6{{( \frac{1}{4} )}^{6}}{{( \frac{3}{4} )}^{10}} $
C) $ {}^{12}C_6{{( \frac{1}{4} )}^{10}}{{( \frac{3}{4} )}^{6}} $
D) $ ^{12}C_6{{( \frac{1}{4} )}^{6}}{{( \frac{3}{4} )}^{6}} $
Show Answer
Answer:
Correct Answer: B
Solution:
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In Binomial distribution, Variance = npq and Mean = np, Variance $ =3=npq, $ Mean $ =\,4=\,np $ Now, $ q=\frac{3}{4},p=\frac{1}{4} $ and $ n=16 $ Probability of success $ =\,{{\,}^{16}}C_6\,{{( \frac{3}{4} )}^{10}}\,{{( \frac{1}{4} )}^{6}} $ .
BETA
