Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Solution:
Given:
[tex]\begin{gathered} p=0.75 \\ n=22 \\ \mu=? \\ \sigma=? \end{gathered}[/tex]Using the formula for the mean and standard deviation of binomial distribution;
[tex]\begin{gathered} \mu=np \\ \text{where;} \\ \mu\text{ is the mean} \\ n\text{ is the number of trials} \\ p\text{ is the probability of success} \\ \\ \\ \text{Also,} \\ \sigma=\sqrt[]{npq} \\ \text{where;} \\ \sigma\text{ is the standard deviation } \\ n\text{ is the number of trials} \\ p\text{ is the probability of success} \\ q\text{ is the probability of failure} \end{gathered}[/tex]Hence, the mean is;
[tex]\begin{gathered} \mu=np \\ \mu=22\times0.75 \\ \mu=16.5 \end{gathered}[/tex]Therefore, the mean is 16.5
The standard deviation is;
[tex]\begin{gathered} \sigma=\sqrt[]{npq} \\ n=22 \\ p=0.75 \\ q=1-0.75=0.25 \\ \\ \sigma=\sqrt[]{22\times0.75\times0.25} \\ \sigma=\sqrt[]{4.125} \\ \sigma=2.031 \end{gathered}[/tex]Therefore, the standard deviation is 2.031
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
