Question

A uniform distribution has a minimum of six and a maximum of ten. A sample of $50$is taken.

Find the $80$th percentile for the sums.

Short answer

The $80$th percentile for the sums is$406.8586$.

Step-by-step solution

Given Information

A uniform distribution has a minimum of six and a maximum of ten. A sample of $50$is taken.

Calculation

We know that the distribution of the sums is $N(400,8.165)$

We have to find $z$from:

$P(\Sigma x<z)=0.8$

$P\left(\frac{\Sigma x-400}{8.165}<\frac{z-400}{8.165}\right)=0.8$

If variable $Z$has a standard normal distribution, then

$P(Z<0.84)=0.8$

Thus, we can find $z$from

$\frac{z-400}{8.165}=0.84$

$z-400=6.8586$

$z=406.8586$.