oday, the waves are crashing onto the beach every 4.7 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.7 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 4.1 seconds after the person arrives is P(x = 4.1) =
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!
Today, the waves are crashing onto the beach every 4.7 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.7 seconds. Round to 4 decimal places where possible.
- The
mean of this distribution is - The standard deviation is
- The
probability that wave will crash onto the beach exactly 4.1 seconds after the person arrives is P(x = 4.1) = - The probability that the wave will crash onto the beach between 1.2 and 4 seconds after the person arrives is P(1.2 < x < 4) =
- The probability that it will take longer than 3.24 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.24) =
- Suppose that the person has already been standing at the shoreline for 0.3 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 4.4 seconds for the wave to crash onto the shoreline. _____
- 57% of the time a person will wait at least how long before the wave crashes in?_____ seconds.
- Find the maximum for the lower
quartile ._____ seconds.
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