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Assume the random variable x is normally distributed with mean mu = 88 and standard deviation...

Question:

Assume the random variable {eq}x {/eq} is normally distributed with mean {eq}\mu = 88 {/eq} and standard deviation {eq}\sigma = 4 {/eq}. Find the indicated probability.

{eq}P(x < 85) {/eq}.

Answer and Explanation:

Given that,

  • Population mean, {eq}\mu = 88 {/eq}
  • Population standard deviation, {eq}\sigma = 4 {/eq}

Now,

The required probability is {eq}P(X < 85). {/eq}

Now,

{eq}P(X < 85) = P(\frac{X-\mu}{\sigma} < \frac{85-\mu}{\sigma})\\ P(X < 85) = P(Z < \frac{85-88}{4})\\ P(X < 85) = P(Z < -0.75)\\ {/eq}

Excel function for the above probability:

=NORMDIST(-0.75,0,1,1)

Now,

{eq}\fbox{P(X < 85) = 0.2266} {/eq}


Learn more about this topic:

Z-Scores in Statistics Explained: Formula, Overview

from Intro to Psychology: Help and Review

Chapter 13 / Lesson 12
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