Answer to Question #160957 in Statistics and Probability for Sunny

Question

There are 18 flights daily from Mumbai to Delhi of Go air, it is known that the probability that any flight arrives late is 0.25. a) what is the probability that one one of the flights is late today?

b) what is the average number of late flights? what is the variance of the number of late flights?

Answer 1

Given,

Total number of available flights (n) = 18

Probability to arrive late flight (p) = 0.25

Probability to not arrive late (q) = (1-0.25) = 0.75

a) Probability that one flight get late by today = $C_0^{18}(0.25)(0.75)^{17}$

$=\frac{1}{4}\times(\frac{3}{4})^{17}$

$=\frac{3^{17}}{4^{18}}$

b)

Average number of late flights $(\mu)=pn =0.25\times 18$

$=4.50$

The variance of number of late flights $(\sigma^2)=npq$

$=\frac{18\times 3}{16}$

$=\frac{27}{8}$