Question

After a large scale earthquake, it is predicted that 15% of all buildings have been structurally compromised.

a) What is the probability that if engineers inspect 20 buildings they will find exactly one that is structurally compromised?

b) What is the probability that if engineers inspect 20 buildings they will find less than 2 that are structurally compromised?

c) What is the probability that if engineers inspect 20 buildings they will find greater than 4 that are structurally compromised?

d) What is the probability that if engineers inspect 20 buildings they will find between 2 and 5 (inclusive) that are structurally compromised?

e) What is the expected number of buildings that an engineer will find structurally compromised if the engineer inspects 20 buildings?

Answer 1

Here p=0.15 which is same for all, events are independent and only two outcomes

Further for each cases n=20 is constant

Hence all the properties of binomial are satisfied

So we will use excel formula to find the required probability

a.

b.

c.

d.

e. Expected value is np=20*0.15=3