A tortoise challenged a hare to a 100-meter race on a track. The tortoise negotiated a 50-meter head start with the hare. When the race started the hare was running at a constant speed of 2.8 meters per second and the tortoise was crawling at a speed of 0.5 meters per second. (They both maintained these speeds for the entire race.) Our goal is to determine who won the race. Read the above problem statement again, then explain in writing on a sheet of paper how you will determine who won the race. Construct a drawing to represent the 100-meter length of the track. Then place the tortoise and hare's starting points on the track. Define the variable t to represent the number of seconds since the start of the race. Write an expression to represent the Tortoise's distance from the starting line in terms of t. Represent the Hare's distance from the starting line in terms of t. Write a formula to represent the distance, d (in meters), that the tortoise is ahead of the hare in terms of t, the amount of time since the start of the race. What is the value of t when the Hare catches up to the Tortoise?
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!
A tortoise challenged a hare to a 100-meter race on a track. The tortoise negotiated a 50-meter head start with the hare. When the race started the hare was running at a constant speed of 2.8 meters per second and the tortoise was crawling at a speed of 0.5 meters per second. (They both maintained these speeds for the entire race.)
Our goal is to determine who won the race.
- Read the above problem statement again, then explain in writing on a sheet of paper how you will determine who won the race.
- Construct a drawing to represent the 100-meter length of the track. Then place the tortoise and hare's starting points on the track.
- Define the variable t to represent the number of seconds since the start of the race.
- Write an expression to represent the Tortoise's distance from the starting line in terms of t.
- Represent the Hare's distance from the starting line in terms of t.
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Write a formula to represent the distance, d (in meters), that the tortoise is ahead of the hare in terms of t, the amount of time since the start of the race.
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What is the value of t when the Hare catches up to the Tortoise?
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How far has the hare run from the start of the race when he catches up to the tortoise?
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On the graph below:
- construct a graph that represents the distance, dd, that the tortoise is ahead of the hare in terms of the number of seconds, tt, since the start of the race.
- Plot the point (10,27)(10,27) on your graph.
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