AshlynPlayz45

12.01.2021 •

Mathematics

DONT ASK ME ANY QUESTIONS THANK YOU

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Ответ:

RoyalGurl01

25.04.2022

Mathematics

Solution :

The test is distributed normally with mean of 72.8 and the standard deviation of 7.3

Finding numerical limits for the D grade.

D grade : Scores below the top 80% and above the bottom 10%.

Let the bottom limit for D grade be $D_1$ and the top limit for D grade be $D_2$ .

First find the bottom numerical limit for a D grade is :

$P(X

$P(X\leq D_1)= 0.10$

$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_1-\mu}{\sigma}\right) = 0.10$

$P\left(Z \leq \frac{D_1-72.8}{7.3}\right) = 0.10$ ..........(1)

From (1)

$\frac{D_1 - 72.8}{7.3} = -1.28$

$D_1 = -1.28(7.3)+72.8$

= 63.45

≈ 64

Now the top numerical limit for D grade :

$P(XD_2)= 0.80$

$1-P(X\leq D_2)= 0.80$

$P(X\leq D_2)= 1-0.80$

$P(X\leq D_2)= 0.20$

$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_2-\mu}{\sigma}\right) = 0.20$

$P\left(Z \leq \frac{D_2-72.8}{7.3}\right) = 0.20$ ..........(2)

From (2)

$\frac{D_2- 72.8}{7.3} = -0.84$

$D_12= -0.84(7.3)+72.8$

= 66.668

≈ 67

Therefore, the numerical limit for a D grade is 64 to 67.

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