Let z be a random variable with a standard normal distribution. Find the indicated probability. What is the probability that P(−0.86 ≤ z ≤ 0)?

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Answer 1 · 2017-03-08T23:30:08

# P(-0.86 < Z < 0 ) = 0.2051#

The standard convention is to use upper case letters to represent random variables.

So #P(-0.86 < Z < 0 )# is represented by the shaded area:

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By symmetry of the standard Normal distribution, this is that same as #P(0 < Z < 0.86)# represented by this shaded area:

enter image source here

And so:

# P(-0.86 < Z < 0 ) = P(0 < Z < 0.86) #
# " "= P(Z < 0.86) - 0.5#
# " "= Phi(0.86) - 0.5#
# " "= 0.8051 - 0.5 \ \ \ # (using tables)
# " "= 0.2051#