Toby’s Trucking company determined that the distance travelled per truck per year is normally distributed, with a mean of 50 thousand miles and a standard deviation of 12 thousand miles. (a) What proportion of trucks can be expected to travel between 34 and 50 thousand miles in a year? Ans: ___________________ (b) What percentage of trucks can be expected to travel more than 60 thousand miles in a year? Ans: ____________________ (c) What percentage of trucks can be expected to travel exactly 50 thousand miles? Ans: ____________________ (d) What percentage of trucks can be expected to travel at the most 49 thousand miles? Ans: ____________________ Paste your working here:
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!
Toby’s Trucking company determined that the distance travelled per truck per year is normally
distributed, with a
(a) What proportion of trucks can be expected to travel between 34 and 50 thousand miles
in a year?
Ans: ___________________
(b) What percentage of trucks can be expected to travel more than 60 thousand miles in a
year?
Ans: ____________________
(c) What percentage of trucks can be expected to travel exactly 50 thousand miles?
Ans: ____________________
(d) What percentage of trucks can be expected to travel at the most 49 thousand miles?
Ans: ____________________
Paste your working here:
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