Paul bowled 6 games today. His scores are shown below.
Game 1: 158 Game 2: 124 Game 3: 110
Game 4: 167 Game 5: 146 Game 6: 165
a. What was Paul's median score for the 6 games? Answer: 152
b. What was Paul's mean score for the 6 games? Answer: 145
c. Paul will bowl one more game. What is the minimum score Paul must achieve in the next game so that his mean score for all 7 games is at least 150? Answer: ?
Please help me with part c
the total points is the mean times the number of games. So, right now he has
870 points for 6 games.
150 points/game * 7 games = 1050 total points
1050-870 = 180
Anything over 180 will raise his average score above 150 for the 7 games.
To find out the minimum score Paul must achieve in the next game so that his mean score for all 7 games is at least 150, we can follow these steps:
Step 1: Calculate the sum of Paul's scores for the first 6 games.
Sum = 158 + 124 + 110 + 167 + 146 + 165 = 870
Step 2: Calculate the mean of Paul's scores for the first 6 games.
Mean = Sum / Number of games = 870 / 6 = 145
Step 3: Calculate the sum of Paul's scores for all 7 games (including the next game).
Total Sum = Sum + Score in the next game
Step 4: Set up an equation to solve for the minimum score Paul must achieve in the next game. Since we want the mean score to be at least 150, the equation would be:
Total Sum / 7 ≥ 150
Plugging in the known values:
(Sum + Score in the next game) / 7 ≥ 150
We can multiply both sides of the inequality by 7 to simplify it:
Sum + Score in the next game ≥ 1050
Substitute the value of the sum calculated in Step 1:
870 + Score in the next game ≥ 1050
Step 5: Solve for the minimum score Paul must achieve in the next game.
Score in the next game ≥ 1050 - 870
Score in the next game ≥ 180
Therefore, the minimum score Paul must achieve in the next game is 180 in order for his mean score for all 7 games to be at least 150.