Confidence Intervals — 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.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=10,s=2,n=25,z^{\ast }=2$$

   Answer: $\left[\frac{46}{5},\frac{54}{5}\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[\frac{46}{5},\frac{54}{5}\right]$$
2. 2.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=50,s=5,n=100,z^{\ast }=2$$

   Answer: $\left[49,51\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[49,51\right]$$
3. 3.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=100,s=12,n=36,z^{\ast }=2$$

   Answer: $\left[96,104\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[96,104\right]$$
4. 4.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=20,s=3,n=16,z^{\ast }=2$$

   Answer: $\left[\frac{37}{2},\frac{43}{2}\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[\frac{37}{2},\frac{43}{2}\right]$$
5. 5.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=75,s=8,n=64,z^{\ast }=2$$

   Answer: $\left[73,77\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[73,77\right]$$
6. 6.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=30,s=10,n=25,z^{\ast }=2$$

   Answer: $\left[26,34\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[26,34\right]$$
7. 7.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=40,s=4,n=16,z^{\ast }=2$$

   Answer: $\left[38,42\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[38,42\right]$$
8. 8.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=60,s=6,n=36,z^{\ast }=2$$

   Answer: $\left[58,62\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[58,62\right]$$
9. 9.

   Find the confidence interval using the supplied critical value.

   $$\bar{x}=80,s=10,n=100,z^{\ast }=2$$

   Answer: $\left[78,82\right]$

   Step-by-step solution

   1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
   2. $$=\left[78,82\right]$$
10. 10.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=25,s=5,n=25,z^{\ast }=2$$

    Answer: $\left[23,27\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[23,27\right]$$
11. 11.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=90,s=9,n=81,z^{\ast }=2$$

    Answer: $\left[88,92\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[88,92\right]$$
12. 12.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=35,s=7,n=49,z^{\ast }=2$$

    Answer: $\left[33,37\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[33,37\right]$$
13. 13.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=120,s=12,n=144,z^{\ast }=2$$

    Answer: $\left[118,122\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[118,122\right]$$
14. 14.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=45,s=3,n=9,z^{\ast }=2$$

    Answer: $\left[43,47\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[43,47\right]$$
15. 15.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=200,s=20,n=400,z^{\ast }=2$$

    Answer: $\left[198,202\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[198,202\right]$$
16. 16.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=15,s=2,n=4,z^{\ast }=2$$

    Answer: $\left[13,17\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[13,17\right]$$
17. 17.

    Find the confidence interval using the supplied critical value.

    $$\bar{x}=70,s=14,n=196,z^{\ast }=2$$

    Answer: $\left[68,72\right]$

    Step-by-step solution

    1. $$\bar{x}\pm z^{\ast }\frac{s}{\sqrt{n}}$$
    2. $$=\left[68,72\right]$$

More from Probability & Statistics

• Counting
• Probability Rules
• Conditional Probability
• Bayes' Rule
• Expected Value
• Binomial Distribution
• Normal Distribution
• Hypothesis Tests
• Linear Regression