Question

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

Find the first quartile for the sums.

Short answer

The first quartile for the sums is $394.53$.

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 the probability:

$P(\Sigma x<z)=0.25$

localid="1649094245554" $P\left(\frac{\Sigma x-400}{8.165}<\frac{z-400}{8.165}\right)=0.25$

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

$P(Z<0.67)=0.75$

Thus, we can find $z$as:

$\frac{z-400}{8.165}=-0.67$

$z-400=-5.47055$

$z=394.53$