Question

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$375$?

Short answer

Result is:

$0.0721$

Step-by-step solution

Given information

we have been given that

${\mu }_X=3.5$

${\sigma }_X=1.71$

$n=Samplesize=100$

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.

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