Question

It is estimated that 27% of births at a particular hospital are by caesarian section. Suppose a sample of 5 births is taken from this hospital.

(a). What is the probability that at most 2 births will be by caesarian section in this hospital?



(b). Write the R code to compute the probability in part (a).



(c). What is the mean number of births delivered by caesarian section in this hospital?



(d). What is the standard deviation of the number births delivered by caesarian section in this hospital?

Answer 1

Given:

p = 0.27

n = 5

The given problem follows binomial distribution with its pmf given as

a) Probability that atmost 2 births will be by caesarian section

The probability that atmost 2 births will be by caesarian section in the hospital is 0.7976

b) R-code

R-code for (a) is pbinom(x,n,p). The function will calcualte the cumulative probability from 0 to x for the given probability p and for the given size of n. Since we need the cumulative probability from 0 to 2 for the size of 5 with probability of 0.27 the function is given as pbinom(2,5,0.27)

c) Mean number of births

Mean in binomial distribution is given as np

Hence, mean = 5*0.27 = 1.35

d) Standard deviation

SD of binomial distribution is given as

Hence,