Question

State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 12 property damage claims involving automobiles are selected at random. A.)What is the probability that two or more claims are made by males under age 25? (Use 3 decimal places.) b.)What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (Use 2 decimal places.)

Answer 1

this is binomial distribution with parameter n=12 and p=0.55

a)

P( two or more claims are made by males under age 25 )=P(X>=2)=1-(P(X=0)+PX=1))

=1-(¹²C₀(0.55)⁰(0.45)¹²+¹²C₁(0.55)¹(0.45)¹¹)=0.999

b)

expected value=np=12*0.55=6.6

standard deviation of the r-probability=sqrt(np(1-p))=1.72