An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given. y 0 1 2 3 p(y) 0.60 0.25 0.10 0.05 What is the probability that among 15 randomly chosen such individuals, at least 10 have no citations? (Round your answer to three decimal places.) What is the probability that among 15 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.) What is the probability that among 15 randomly chosen such individuals, the number that have at least one citation is between 5 and 10, inclusive? ("Between a and b, inclusive" is equivalent to (a ≤ X ≤ b). Round your answer to three 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!
| y | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
|
p(y)
|
0.60 | 0.25 | 0.10 | 0.05 |
What is the
What is the probability that among 15 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.)
What is the probability that among 15 randomly chosen such individuals, the number that have at least one citation is between 5 and 10, inclusive? ("Between a and b, inclusive" is equivalent to
Round your answer to three decimal places.)
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