(b) what is the probability that seven or more claims are made by males under age 25? (use 3 decimal places) (c) what is the expected nunber of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (use two decimal places)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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State Farm Insurance studies show that in Colorado, 45% of the auto insurance claims submitted for property damage were submitted by 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.
0.25
0.25
0.2
0.2
0.15
Po 0.15
Plt)
01-
0.1
0.05
0.05
0'012 3 4 5 6789 10
0123 45 6 7 89 10
0.6
0.2
0.5
0.15
04
Pr)
P() 0.3
0.1
0.2
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