Andre sets up a rain gauge to measure rainfall in his back yard. On Tuesday, it rains off and on all day. He starts at 10 a.m. with an empty gauge when it starts to rain. Two hours later, he checks, and the gauge has 2 cm of water in it. It starts raining even harder, and at 4 p.m., the rain stops, so Andre checks the rain gauge and finds it has 10 cm of water in it. While checking it, he accidentally knocks the rain gauge over and spills most of the water, leaving only 3 cm of water in the rain gauge. When he checks for the last time at 5 p.m., there is no change. a. Which of the two graphs could represent Andre’s story? Explain your reasoning. b. Label the axes of the correct graph with appropriate units. c. Use the graph to determine how much total rain fell on Tuesday.
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!
Andre sets up a rain gauge to measure rainfall in his back yard. On Tuesday, it rains off
and on all day.
He starts at 10 a.m. with an empty gauge when it starts to rain.
Two hours later, he checks, and the gauge has 2 cm of water in it.
It starts raining even harder, and at 4 p.m., the rain stops, so Andre checks the rain
gauge and finds it has 10 cm of water in it.
While checking it, he accidentally knocks the rain gauge over and spills most of the
water, leaving only 3 cm of water in the rain gauge.
When he checks for the last time at 5 p.m., there is no change.
a. Which of the two graphs could represent Andre’s story? Explain your reasoning.
b. Label the axes of the correct graph with appropriate units.
c. Use the graph to determine how much total rain fell on Tuesday.
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