# Thread: rolling a die ...

1. ## rolling a die ...

greets

2. Originally Posted by shirel
Exercise:

A die is rolled 600 times. how many times does face 5 show up?
Specify a reasonable range. Discuss why you prefer that one over other possible estimates.
how certain is your estimate? For which range would you be absolutely certain?

thanks for showing me your ideas, thoughts, explanations, calculations..

greets
of times a 5 will come up.

Now 600 times is a large number of rolls so we may as well use the normal
approximation to the binaomial distribution, in this case it will have mean:

$\displaystyle m=Np = 600 \times (1/6) = 100$

and standard deviation:

$\displaystyle \sqrt{Np(1-p)} = \sqrt{600(1/6)(5/6)} \approx 9.13$

So you would expect the number of 5's to be $\displaystyle 100 \pm k \times 9.13$, where
the value of $\displaystyle k$ is chossen by you depending on what confidence you want
that the actual number lies in the interval, often a value of $\displaystyle k=1.96$ is used.

RonL