A certain delivery truck carries loads that follow a normal distribution with an average weight of 3500 pounds and a standard deviation of 700 pounds. For the following, show your graph and calculator commands. What load weight represents the top 30% of loads? What proportion of loads are less than 3000 pounds? What two load weights hold the middle 80% of loads? Find the 90th percentile of load weights. If a load is more than 6000 pounds, it is considered unsafe. What proportion of loads were unsafe? Using probability, would it be unusual for the delivery truck to carry an unsafe load?
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 certain delivery truck carries loads that follow a
- What load weight represents the top 30% of loads?
- What proportion of loads are less than 3000 pounds?
- What two load weights hold the middle 80% of loads?
- Find the 90th percentile of load weights.
- If a load is more than 6000 pounds, it is considered unsafe. What proportion of loads were unsafe? Using probability, would it be unusual for the delivery truck to carry an unsafe load?
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