Probability The most important function in probability and statistics is the density function for the standard normal distribution, which is the familiar bell-shaped curve. The function is 1 f(x) = V2T (a) The area under this curve between x = -1 and x = 1 represents the probability that a normal random vari- able is within 1 standard deviation of the mean. Find this probability. (b) Find the area under this curve between x = -2 and x = 2, which represents the probability that a normal random variable is within 2 standard deviations of the mean. (c) Find the probability that a normal random variable is with- in 3 standard deviations of the mean. 5/-

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Probability The most important function in probability
and statistics is the density function for the standard normal
distribution, which is the familiar bell-shaped curve. The
function is
1
f(x) =
V2T
(a) The area under this curve between x = -1 and x = 1
represents the probability that a normal random vari-
able is within 1 standard deviation of the mean. Find this
probability.
(b) Find the area under this curve between x = -2 and
x = 2, which represents the probability that a normal
random variable is within 2 standard deviations of the
mean.
(c) Find the probability that a normal random variable is with-
in 3 standard deviations of the mean.
5/-
Transcribed Image Text:Probability The most important function in probability and statistics is the density function for the standard normal distribution, which is the familiar bell-shaped curve. The function is 1 f(x) = V2T (a) The area under this curve between x = -1 and x = 1 represents the probability that a normal random vari- able is within 1 standard deviation of the mean. Find this probability. (b) Find the area under this curve between x = -2 and x = 2, which represents the probability that a normal random variable is within 2 standard deviations of the mean. (c) Find the probability that a normal random variable is with- in 3 standard deviations of the mean. 5/-
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