zion's drive to work has 4 lights. she is trying to make sure she is on time to work every day, so for a month she tracked how many times she hit a red light out of her 4 lights and created the model below showing the probability of hitting anywhere from zero to 4 red lights X 0 1 2 3 4 P(X) .27 .35 .17 .16 what is the probability of hitting no red lights? what is the expected average number of red lights she would hit every day? what is the expected standard deviation of red lights?
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!
zion's drive to work has 4 lights. she is trying to make sure she is on time to work every day, so for a month she tracked how many times she hit a red light out of her 4 lights and created the model below showing the probability of hitting anywhere from zero to 4 red lights
| X | 0 | 1 | 2 | 3 | 4 |
| P(X) | .27 | .35 | .17 | .16 |
what is the probability of hitting no red lights?
what is the expected average number of red lights she would hit every day?
what is the expected standard deviation of red lights?
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