The number of trials n and the probability of success p is given for different binomial distributions. Arrange them in increasing order of their variance:

Choose the correct answer from the options given below:

Correct option is C

Variance for a binomial distribution is calculated using the formula:
Variance=n⋅p⋅(1−p)\text{Variance} = n \cdot p \cdot (1 - p)Variance=n⋅p⋅(1−p)
Calculate the variance for each option:
1. Option (A):
Variance= 15⋅0.4⋅ (1−0.4) =15⋅0.4⋅0.6=3.6
2. Option (B):
Variance=12⋅0.5⋅ (1−0.5) =12⋅0.5⋅0.5=3.0
3. Option (C):
Variance=16⋅0.7⋅ (1−0.7) =16⋅0.7⋅0.3=3.36
4. Option (D):
Variance=18⋅0.6⋅ (1−0.6) =18⋅0.6⋅0.4=4.32, Now, arrange them in increasing order of their variance: Thus, the correct order is (B), (C), (A), (D).
Additional Insights: · The variance of a binomial distribution reflects the spread of possible successes in n trials.
· For larger n, even small changes in p can significantly affect the variance.