The average number of miles driven on a full tank of gas in a certain model car before its low-fuel light comes on is 385. Assume this mileage follows the normal distribution with a standard deviation of 31 miles. What is the probability that, before the low-fuel light comes on, the car will travel exactly 359 miles on the next tank of gas? Note that there in no area under a curve at a specific value. That is, if you think of a rectangle as the area under the curve, the width would be zero and so the area would be zero. With this information, find the probability.
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!
The average number of miles driven on a full tank of gas in a certain model car before its low-fuel light comes on is 385. Assume this mileage follows the
What is the
Note that there in no area under a curve at a specific value. That is, if you think of a rectangle as the area under the curve, the width would be zero and so the area would be zero. With this information, find the probability.
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