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Answers without the blur. Sign up and see all textbooks for free! Q. 10

Expert-verified Found in: Page 668 ### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339 # Let $X$ represent the score when a fair six-sided die is rolled. For this random variable,${\mu }_{X}=3.5$ and ${\sigma }_{X}=1.71$. If the die is rolled $100$ times, what is the approximate probability that the total score is at least $375$?

Result is:

$0.0721$

See the step by step solution

## Step 1: Given information

we have been given that

${\mu }_{X}=3.5$

${\sigma }_{X}=1.71$

$n=Samplesize=100$

## Step 2: Simplify

The mean score is the total score divided by the sample

$\overline{x}=\frac{Totalscore}{n}$

The Z score is the value decreased by the mean

$z=\frac{x-\mu }{\sigma /\sqrt{n}}=\frac{3.75-3.5}{1.71/\sqrt{100}}\approx 1.47$

Row is starting with $1.4$ and column is starting with 0.06 of the table.

$P\left(\overline{X}\ge 3.75\right)=P\left(Z>1.46\right)=1-P\left(Z<1.46\right)=1-0.9279=0.0721$

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