What is the distribution of X? X What is the distribution of ? - What is the distribution of
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 time to run the 5K fun run is 20 minutes and the standard deviation is 2.5 minutes. 42 runners
are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and
assume a normal distribution.
a. What is the distribution of X? X - NG
b. What is the distribution of x? a - N(
c. What is the distribution of æ? -
N(
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
19.8213 and 20.1213 minutes.
e. For the 42 runners, find the probability that their average time is between 19.8213 and 20.1213
minutes.
f. Find the probability that the randomly selected 42 person team will have a total time less than
848.4.
g. For part e) and f), is the assumption of normal necessary? O NoO Yes
h. The top 20% of all 42 person team relay races will compete in the championship round. These are the
20% lowest times. What is the longest total time that a relay team can have and still make it to the
championship round?
minutes
Hint:
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