Question

# State Farm Insurance studies show that in Colorado, 50% of the auto insurance claims submitted for...

State Farm Insurance studies show that in Colorado, 50% 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) Let r be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities.

(b) What is the probability that six or more claims are made by males under age 25? (Use 3 decimal places.)

(c) 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.)

 μ σ

Solution-A:

x values ranges from 0 to 12

n=12

p=0.50

Rcode to get histogram:

library(tigerstats)
pbinomGC(c(0,12),region="between",size=12,prob=0.5,graph=TRUE)

Solution-b:

need to find

P(X>=6)

X values from 6 ,7,8,9,10,11,12

Rcode:

pbinomGC(c(6,12),region="between",size=12,prob=0.5,graph=TRUE)

probability that six or more claims are made by males under age 25=0.613

Solution-c:

mean=n*p=12*0.50=6

standard deviation=sqrt(n*p*q)

=sqrt(12*0.5*(1-0.5)

=1.732051

=1.73

mean=6

standard deviation=1.73

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