Unformatted text preview: calculated by
ba
.
dc
The mean and standard deviation of a uniformly distributed random variable is given by
c+d
dc
µ=
ß=
.
2
12
P(a < X < b) = 46 Example 1 Spinning a Dial Suppose that you spin the dial shown below so that it comes to
rest at a random position. Model this with a suitable distribution, and use it to find the
probability that the dial will land somewhere between 5˚ and 300˚.
0 270 90 180 The Normal Distribution
A normal density function is a function of the form
 f(x) = 1
e
ß 2π (xµ)2
2ß2 . µ = Mean
ß = standard deviation
The standard normal distribution has µ = 0 and ß = 1. We use Z rather than X to refer
to the associated random variable.
Tables The following tables give the probabilities P(Z ≤ z).
Note Excel formula for this is =NORMSDIST(z) 47...
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 Spring '13
 Herbret
 Statistics, Normal Distribution, Probability distribution, Probability theory, probability density function, density function

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