Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. xx P(x)P(x) 0 0.3377 1 0.3347 2 0.1744 3 0.0605 4 0.0464 5 0.0463 6+ 0.0000 a) What is the probability that a randomly selected person has received four tickets in a three-year period? P(x=4)=P(x=4)= b) What is the probability that a randomly selected person has received four or more tickets in a three-year period? P(x≥4)=P(x≥4)= c) What is the probability that a randomly selected person has received more than four tickets in a three-year period? P(x>4)=P(x>4)= d) Would it be unusual to randomly select a person who has received four tickets in a three-year period? Yes No e) Which probability should we use to determine whether or not it is unusual to randomly select a person who has received four tickets in a three-year period? P(x=4)P(x=4) P(x>4)P(x>4) P(x≥4)
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!
Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)P(x) represents the
| xx | P(x)P(x) |
|---|---|
| 0 | 0.3377 |
| 1 | 0.3347 |
| 2 | 0.1744 |
| 3 | 0.0605 |
| 4 | 0.0464 |
| 5 | 0.0463 |
| 6+ | 0.0000 |
a) What is the probability that a randomly selected person has received four tickets in a three-year period?
P(x=4)=P(x=4)=
b) What is the probability that a randomly selected person has received four or more tickets in a three-year period?
P(x≥4)=P(x≥4)=
c) What is the probability that a randomly selected person has received more than four tickets in a three-year period?
P(x>4)=P(x>4)=
d) Would it be unusual to randomly select a person who has received four tickets in a three-year period?
- Yes
- No
e) Which probability should we use to determine whether or not it is unusual to randomly select a person who has received four tickets in a three-year period?
- P(x=4)P(x=4)
- P(x>4)P(x>4)
- P(x≥4)
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