Normal Distribution — Practice Problems and Worked Solutions

The formulas you need here

17 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Standardize the observation.

   $$\mu =70,\sigma =10,x=80$$

   Answer: $1$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=1$$
2. 2.

   Standardize the observation.

   $$\mu =100,\sigma =15,x=130$$

   Answer: $2$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=2$$
3. 3.

   Standardize the observation.

   $$\mu =50,\sigma =5,x=45$$

   Answer: $-1$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=-1$$
4. 4.

   Standardize the observation.

   $$\mu =20,\sigma =4,x=26$$

   Answer: $\frac{3}{2}$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=\frac{3}{2}$$
5. 5.

   Standardize the observation.

   $$\mu =500,\sigma =50,x=425$$

   Answer: $-\frac{3}{2}$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=-\frac{3}{2}$$
6. 6.

   Standardize the observation.

   $$\mu =12,\sigma =3,x=18$$

   Answer: $2$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=2$$
7. 7.

   Standardize the observation.

   $$\mu =60,\sigma =5,x=75$$

   Answer: $3$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=3$$
8. 8.

   Standardize the observation.

   $$\mu =80,\sigma =10,x=65$$

   Answer: $-\frac{3}{2}$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=-\frac{3}{2}$$
9. 9.

   Standardize the observation.

   $$\mu =200,\sigma =25,x=250$$

   Answer: $2$

   Step-by-step solution

   1. $$z=\frac{x-\mu }{\sigma }$$
   2. $$=2$$
10. 10.

    Standardize the observation.

    $$\mu =40,\sigma =8,x=24$$

    Answer: $-2$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=-2$$
11. 11.

    Standardize the observation.

    $$\mu =150,\sigma =20,x=190$$

    Answer: $2$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=2$$
12. 12.

    Standardize the observation.

    $$\mu =25,\sigma =5,x=40$$

    Answer: $3$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=3$$
13. 13.

    Standardize the observation.

    $$\mu =90,\sigma =12,x=66$$

    Answer: $-2$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=-2$$
14. 14.

    Standardize the observation.

    $$\mu =300,\sigma =30,x=240$$

    Answer: $-2$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=-2$$
15. 15.

    Standardize the observation.

    $$\mu =15,\sigma =3,x=24$$

    Answer: $3$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=3$$
16. 16.

    Standardize the observation.

    $$\mu =55,\sigma =11,x=88$$

    Answer: $3$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=3$$
17. 17.

    Standardize the observation.

    $$\mu =120,\sigma =15,x=165$$

    Answer: $3$

    Step-by-step solution

    1. $$z=\frac{x-\mu }{\sigma }$$
    2. $$=3$$

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