Statistics I20795 marksNumerical: binomial distribution consistencyDiscrete distributions
The mean and variance of the number of flights arriving late in a day are 2 and 1.6 respectively. Assuming binomial distribution, are those values consistent? If yes, find the probability that (i) none of the flights are late today and (ii) at least one flight is late today.
The mean and variance of the number of flights arriving late in a day are 2 and 1.6 respectively. Assuming binomial distribution, are those values consistent? If yes, find the probability that (i) none of the flights are late today and (ii) at least one flight is late today. [5]
- Mean $= np = 2$ - Variance $= npq = 1.6$ For a binomial distribution, variance < mean always (since $q < 1$). Here mean $= 2$, variance $= 1.6$, and $1.6 < 2$, so the values are consistent. $$q = \frac{npq}{np} = \frac{1.6}{2} = 0.8$$ $$p = 1 - q = 0.2$$ $$np = 2 \Rightarrow n = \frac{2}{0.2} =...