A safety engineer claims that only 40 of all workers wear sa

A safety engineer claims that only 40% of all workers wear safety helmets when they eat

lunch at the workplace. Assuming that the claim is right, find the probability that 4 of 6

workers randomly chosen will be wearing their helmets while having lunch at the workplace

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X = 4 ) = ( 6 4 ) * ( 0.4^4) * ( 1 - 0.4 )^2
= 0.1382