Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To solve the given problem, we need to determine two things: the sample mean of the ratings and the proportion of ratings that are higher than the sample mean.
1. Calculate the Sample Mean:
- First, list all the ratings from the table:
[tex]\[ 2, 5, 4, 3, 3, 3, 1, 3, 2, 1, 2, 4, 3, 3, 4, 4, 4, 5, 5, 4 \][/tex]
- Next, sum these ratings:
[tex]\[ 2 + 5 + 4 + 3 + 3 + 3 + 1 + 3 + 2 + 1 + 2 + 4 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 4 = 64 \][/tex]
- There are 20 ratings in total.
- The sample mean is calculated by dividing the sum by the number of ratings, which is:
[tex]\[ \text{Sample Mean} = \frac{64}{20} = 3.25 \][/tex]
2. Determine the Proportion of Ratings Higher than the Sample Mean:
- Now we need to count how many ratings are higher than the sample mean (3.25).
- The ratings higher than 3.25 from the list are: 5, 4, 4, 4, 4, 5, 5, 4. There are 9 such ratings.
- To find the proportion, divide the number of ratings higher than the sample mean by the total number of ratings:
[tex]\[ \text{Proportion Higher} = \frac{9}{20} = 0.45 \][/tex]
Based on the calculations, the answers are as follows:
The sample mean is [tex]\( \boxed{3.25} \)[/tex].
The proportion of moviegoers in the sample who gave a rating higher than the sample mean is [tex]\( \boxed{0.45} \)[/tex].
1. Calculate the Sample Mean:
- First, list all the ratings from the table:
[tex]\[ 2, 5, 4, 3, 3, 3, 1, 3, 2, 1, 2, 4, 3, 3, 4, 4, 4, 5, 5, 4 \][/tex]
- Next, sum these ratings:
[tex]\[ 2 + 5 + 4 + 3 + 3 + 3 + 1 + 3 + 2 + 1 + 2 + 4 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 4 = 64 \][/tex]
- There are 20 ratings in total.
- The sample mean is calculated by dividing the sum by the number of ratings, which is:
[tex]\[ \text{Sample Mean} = \frac{64}{20} = 3.25 \][/tex]
2. Determine the Proportion of Ratings Higher than the Sample Mean:
- Now we need to count how many ratings are higher than the sample mean (3.25).
- The ratings higher than 3.25 from the list are: 5, 4, 4, 4, 4, 5, 5, 4. There are 9 such ratings.
- To find the proportion, divide the number of ratings higher than the sample mean by the total number of ratings:
[tex]\[ \text{Proportion Higher} = \frac{9}{20} = 0.45 \][/tex]
Based on the calculations, the answers are as follows:
The sample mean is [tex]\( \boxed{3.25} \)[/tex].
The proportion of moviegoers in the sample who gave a rating higher than the sample mean is [tex]\( \boxed{0.45} \)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.