Question

Make Excel do all calculations

An insurance company has found that 10% of its claims are for damages resulting from burglaries. A random sample of 20 claims is pulled.

a. What is the expected number(mean) that will be claimed for damages resulting from burglaries?

b. What is the standard deviation?

Use Excel function BINOMDIST (watch podcast) as appropriate in the following questions.

c. What is the probability that exactly 5 of the 20 will contain claims that are for burglary damages?

d. What is the probability that fewer than 5 will contain claims that are for burglary damages?

e. What is the probability that at least 5 will contain claims that are for burglary damages?

Answer 1

Define a random variable X (no. of damages for burglaries) ~ Binomial(n=20, p=0.10)

(a)

Expected number of claims for burlaries = n.p = 20*0.1 = 2

(b)

Standard deviation = √{n.p.(1 - p)} = SQRT(20*0.1*(1 - 0.1)) = 1.342

(c)

P(X=5) = BINOMDIST(5,20,0.1,0) = 0.0319

(d)

P(X < 5) = P(X <= 4) = BINOMDIST(4,20,0.1,1) = 0.9568

(e)

P(X >= 5) = 1 - P(X <= 4) = 1 - 0.9568 = 0.0432