Answer:
59 to 66
Step-by-step explanation:
Mean test scores = u = 74.2
Standard Deviation =
= 9.6
According to the given data, following is the range of grades:
Grade A: 85% to 100%
Grade B: 55% to 85%
Grade C: 19% to 55%
Grade D: 6% to 19%
Grade F: 0% to 6%
So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.
6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)
The formula for z score is:

For z = -1.56, we get:

For z = -0.88, we get:

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)
Answer:
2.956
Step-by-step explanation:

= 
= 2.956
Answer:
![6^{\frac{1}{5} }=\sqrt[5]{6}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B1%7D%7B5%7D%20%7D%3D%5Csqrt%5B5%5D%7B6%7D)
![6^{\frac{7}{5} }=\sqrt[5]{6^7}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B7%7D%7B5%7D%20%7D%3D%5Csqrt%5B5%5D%7B6%5E7%7D)
![6^{\frac{1}{6} }=\sqrt[6]{6}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B1%7D%7B6%7D%20%7D%3D%5Csqrt%5B6%5D%7B6%7D)
![7^{\frac{1}{2} }=\sqrt[2]{7}](https://tex.z-dn.net/?f=7%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%3D%5Csqrt%5B2%5D%7B7%7D)
![7^{\frac{5}{2} }=\sqrt[2]{7^5}](https://tex.z-dn.net/?f=7%5E%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%3D%5Csqrt%5B2%5D%7B7%5E5%7D)
![6^{\frac{9}{2} }=\sqrt[2]{6^9}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B9%7D%7B2%7D%20%7D%3D%5Csqrt%5B2%5D%7B6%5E9%7D)
Step-by-step explanation:
A radical is the root operation for n roots such as square root or cuberoot in the form
. A fraction exponent
can be converted to the radical form.
![6^{\frac{1}{5} }=\sqrt[5]{6}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B1%7D%7B5%7D%20%7D%3D%5Csqrt%5B5%5D%7B6%7D)
![6^{\frac{7}{5} }=\sqrt[5]{6^7}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B7%7D%7B5%7D%20%7D%3D%5Csqrt%5B5%5D%7B6%5E7%7D)
![6^{\frac{1}{6} }=\sqrt[6]{6}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B1%7D%7B6%7D%20%7D%3D%5Csqrt%5B6%5D%7B6%7D)
![7^{\frac{1}{2} }=\sqrt[2]{7}](https://tex.z-dn.net/?f=7%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%3D%5Csqrt%5B2%5D%7B7%7D)
![7^{\frac{5}{2} }=\sqrt[2]{7^5}](https://tex.z-dn.net/?f=7%5E%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%3D%5Csqrt%5B2%5D%7B7%5E5%7D)
![6^{\frac{9}{2} }=\sqrt[2]{6^9}](https://tex.z-dn.net/?f=6%5E%7B%5Cfrac%7B9%7D%7B2%7D%20%7D%3D%5Csqrt%5B2%5D%7B6%5E9%7D)