Verify whether the given table represents a probability distribution. In those cases where a probability distribution is described, find the mean and standard deviation. NOTE: The Rounding Rule for the mean and standard deviation: They should be rounded to one more decimal place than occurs in the raw data. For a group of four students, the number y who takes the Calculus II class next semester is given by this table. y P(y) 0 0.5131 1 0.3139 2 0.0624 3 0.1102 4 0.2002 Probability distribution with μ=0.4 and σ=0.4 Probability distribution with μ=0.6 and σ=0.1 Probability distribution with μ=0.6 and σ=0.3 Probability distribution with μ=0.7 and σ=0.4
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!
Verify whether the given table represents a
For a group of four students, the number y who takes the Calculus II class next semester is given by this table.
y P(y)
0 0.5131
1 0.3139
2 0.0624
3 0.1102
4 0.2002
Probability distribution with μ=0.4 and σ=0.4
Probability distribution with μ=0.6 and σ=0.1
Probability distribution with μ=0.6 and σ=0.3
Probability distribution with μ=0.7 and σ=0.4
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