Mean and variance for four different Binomial distributions with parameters n (number of trials) and p (probability of success) are given in A-D below. Compute the number of trials (n) for each Binomial distribution and arrange in ascending order. Choose the correct answer from the options given below :
1.Mean = 2.1, Variance = 1.47
2.Mean = 2.0, Variance = 1.20
3.Mean = 4.0, Variance = 2.00
4.Mean = 3.6, Variance = 1.44
A3, 4, 1, 2
B1, 3, 2, 4
C4, 1, 3, 2
D2, 4, 1, 3 ✓ Correct
Correct answer: (D) 2, 4, 1, 3
Explanation
The ascending order of n is 5, 6, 7, 8 giving 2, 4, 1, 3.
For a Binomial, mean = np and variance = npq, so q = variance/mean and p = 1 - q.
Then n = mean / p.
Item 1 : q = 1.47/2.1 = 0.7, p = 0.3, n = 2.1/0.3 = 7.
Item 2 : n = 2.0/0.4 = 5 ; item 3 : n = 4.0/0.5 = 8.
Item 4 : n = 3.6/0.6 = 6, so ascending n : 5, 6, 7, 8 = items 2, 4, 1, 3.
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