Learn / Library / Statistics

Sum of many dice

StatisticsMedium

A fair $6$ -sided die is rolled $300$ times, with independent rolls. Using the normal approximation without continuity correction, what is the $z$ -score of a total of $1100$ ? Round to $2$ decimal places.

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

One roll has variance $E [X^{2}] - E [X]^{2}$ ; variances add.

Solution

One roll has mean $3.5$ and variance $\frac{91}{6} - \frac{49}{4} = \frac{35}{12}$ .
For $300$ rolls the mean total is $300 \times 3.5 = 1050$ .
The variance of the total is $300 \times \frac{35}{12} = 875$ , so the standard deviation is $875 \approx 29.58$ .
The $z$ -score is $(1100 - 1050) \div 29.58 \approx 1.69$ .
The answer is $1.69$ .

Answer: $\approx 1.69$

Next question Back to the library