Mathematics: What is the mean of this discrete random variable?

What is the mean of this discrete random variable?

supercutedonuf3753

19.04.2022

The weight that separate the top 8% by 5.2605 and the weight that separate bottom 8% by 5.1195.

Step-by-step explanation:

We are given that

Mean, $\mu=5.19$

Standard deviation, $\sigma=0.05$

We have to find the two weights that separate the top 8% and the bottom 8%.

Let x1 and x2 the two weights that separate the top 8% and the bottom 8%.

Z-value for p-value =0.08 = -1.41

For 8% bottom

$Z=\frac{x_1-\mu}{\sigma}=-1.41$

$\frac{x_1-5.19}{0.05}=-1.41$

$x_1-5.19=-1.41\times 0.05$

$x_1=-1.41\times 0.05+5.19$

x_1=5.1195

For 8% top

p-Value=1-0.08=0.92

Z- value=1.41

Now,

$\frac{x_2-5.19}{0.05}=1.41$

$x_2-5.19=1.41\times 0.05$

$x_2=1.41\times 0.05+5.19$

x_2=5.2605

(x1,x2)=(5.1195,5.2605)

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