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)
ANSWER"
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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