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Q. 10

Expert-verifiedFound in: Page 668

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:

$0.0721$

we have been given that

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

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

$n=Samplesize=100$

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.

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

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