Question

Find the probability that the sums will fall between the $z-$scores $–2$ and $1$.

Short answer

The required probability is$0.8186$.

Step-by-step solution

Given Information

Given in the question that, the sample size of $100$is randomly drowned from cans of the same soda with mean$39.01$and the standard deviation is$0.5$

Explanation

The sum that is $z-$score$-2$standard deviation is:

$\sum X=\left(n\right)\left({\mu }_X\right)+\left(z\right)\left(\sqrt{n}\right)\left({\sigma }_X\right)$

$=100\times 39.01-2\times \sqrt{100}\times 0.5$

$=3891$

Let's compute the sum that is $z-score-1$standard deviation is:

$\mathrm{\Sigma }X=\left(n\right)\left({\mu }_X\right)+\left(z\right)\left(\sqrt{n}\right)\left({\sigma }_x\right)$

$=100\times 39.01+1\times \sqrt{100}\times 0.5$

$=3906$

Using Ti-83 calculator

To find the proportion of sums, we'll use the Ti-83 calculator:

To do so, go to 2nd, then DISTR.

Then, scroll down to the normalcdf option and fill in the required information.

After that, press the calculator's enter button to get the result.