Winona needs to average 5.8 points from 14 judges to win the competition. The mean score of 13 judges was 5.9. What is the lowest score she can receive from the fourteenth judge and still win?
I have no idea. Please help. Thanks
Mean = ∑x/n
5.8 = (13*5.9 + x)/14
Solve for x.
To determine the lowest score Winona can receive from the fourteenth judge and still win the competition, we need to consider the average score she needs to achieve and the scores she has already received.
Given:
- Winona needs to average 5.8 points from 14 judges to win the competition.
- The mean score of 13 judges was 5.9.
To find the lowest score she can receive, we can start by calculating the total points Winona needs to achieve:
Total points needed = Average points * Total number of judges
Total points needed = 5.8 * 14
Total points needed = 81.2
Next, we can calculate the total points Winona has already received from the first 13 judges:
Total points received = Average score * Total number of judges - (Average score - Actual scores of the first 13 judges)
Since the mean score of the first 13 judges was 5.9, and we know the total number of judges is 13, we can calculate the points received from the first 13 judges:
Total points received = 5.9 * 13
Total points received = 76.7
To find the lowest score Winona can receive and still win, we subtract the points already received from the total points needed:
Lowest score Winona can receive = Total points needed - Total points received
Lowest score Winona can receive = 81.2 - 76.7
Lowest score Winona can receive = 4.5
Therefore, the lowest score Winona can receive from the fourteenth judge and still win the competition is 4.5 points.