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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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

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

Explanation:

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

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

enter image source here

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

enter image source here

And so:

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

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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)?

1 Answer

Explanation:

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