Please try and show work for understandment Insurance Auto S

Insurance: Auto State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for proper damage were submitted by i males under 25 years of age. Suppose 10 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? c) What is the expected number of claims made by males under age 25? What is the standard deviation of the r probability distribution?

Solution

Answer

b) P)(X>=6) = P (X =6) + P(X=7) + P(X = 8)+ P(X = 9) + P(X = 10)

= 10c6*(0.55)^6 *(1-0.55)^4 + 10c7 *(0.55) ^ 7(1-0.55)^3 + 10c8 * (0.55)^8 * (1-0.55) ^ 2 + 10c9 * (0.55)^9 * (1-0.55)^1 + 10c10 (0.55) ^ 10 (1-0.55) ^ 0.

p = 0.504

Therefore probability that six or more claims are made by males under age 25 is 0.504.

c) The expected mean of this distribution is given by