A coach tells his little league players that hitting a 0.275 batting average, within 7% percentage error, means that they had a really great season. Seven year old Tommy ended the season hitting a 0.258 batting average. According to his coach, did he have a great season?
0.07 * 0.275 = 0.019
0.275 - 0.019 = 0.256
Yes. Tommy had a great season.
Well, Tommy certainly made a good attempt at having a great season! But if we calculate the 7% percentage error, we find that he fell slightly short. So, Tommy didn't have a great season statistically speaking, but hey, there's always next time!
To determine if Tommy had a great season according to his coach's criteria, we need to check if Tommy's batting average falls within 7% of the desired average of 0.275.
First, let's calculate the upper and lower limits of the acceptable range:
Upper limit = 0.275 + (0.275 * 0.07)
= 0.275 + 0.01925
≈ 0.29425
Lower limit = 0.275 - (0.275 * 0.07)
= 0.275 - 0.01925
≈ 0.25575
Since Tommy's batting average of 0.258 falls within the range of 0.25575 to 0.29425, he did have a great season according to his coach's criteria.
To determine whether Tommy had a great season according to his coach's criteria, we need to calculate the percentage difference between Tommy's batting average and the desired batting average.
First, let's find the desired batting average. The coach considers a batting average of 0.275 as a great season, with 7% percentage error allowed. To calculate the acceptable range for the batting average, we multiply 0.275 by 7%: 0.275 * 0.07 = 0.01925.
Now, we can determine the acceptable range for the batting average. The lower end of the range is the desired batting average minus the acceptable error, and the upper end is the desired batting average plus the acceptable error.
Lower end: 0.275 - 0.01925 = 0.25575
Upper end: 0.275 + 0.01925 = 0.29425
Tommy's batting average is 0.258, which falls within the acceptable range of 0.25575 to 0.29425. Therefore, according to his coach's criteria, Tommy did have a great season.