Mathematics: I need help with this somebody help me out!!

I need help with this somebody help me out!!

Ответ:

mayhy100

22.10.2021

Mathematics

6.7 -0.674 *1.1 =5.96

6.7 +0.674 *1.1 =7.44

Step-by-step explanation:

Let X the random variable that represent the head breadths of a population, and for this case we know the distribution for X is given by:

$X \sim N(6.7,1.1)$

Where $\mu=6.7$ and $\sigma=1.1$

We want the range of the middle 50% values on the distribution. Since the normal distribution is symmetrical we know that in the tails we need to have the other 50% and on each tail 25% by symmetry.

We can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

The critical values that accumulates 0.25 of the area on each tail we got:

$z_{crit}= \pm 0.674$

And if we solve x from the z score we got:

$x = \mu \pm z \sigma$

And replacing we got:

6.7 -0.674 *1.1 =5.96

6.7 +0.674 *1.1 =7.44

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