Answer:
a) About 68% of the data would be between 305 grams to 395 grams
b) About 95% of organs weighs between 260 grams and 440 grams
c)About 5% of organs weighs less than 260 grams or more than 440 grams
d) About 97% of organs weighs between 215 grams and 440 grams
Step-by-step explanation:
The empirical rule formula:
1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ
(a) About 68% of organs will be between what weights?
We would be applying the First rule of the Empirical formula to this.
68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
Mean = 350 grams
Standard deviation = 45 grams
Hence,
350 grams - 45 grams
= 305 grams
350grams + 45grams
= 395 grams
Therefore about 68% of the data would be between 305 grams to 395 grams
(b) What percentage of organs weighs between 260 grams and 440 grams?
Let try the second rule
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Mean = 350 grams
Standard deviation = 45 grams
μ - 2σ
= 350 - 2(45)
= 350 - 90
= 260
μ + 2σ
= 350 + 2(45)
= 350 + 90
= 440
Therefore, about 95% of organs weighs between 260 grams and 440 grams
(c) What percentage of organs weighs less than 260 grams or more than 440 grams?
Let try the second rule
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Mean = 350 grams
Standard deviation = 45 grams
μ + 2σ
= 350 - 2(45)
= 350 - 90
= 260
μ + 2σ
= 350 + 2(45)
= 350 + 90
= 440
Since, about 95% of organs weighs between 260 grams and 440 grams, the percentage of organs weighs less than 260 grams or more than 440 grams is calculated as:
100% - 95%
= 5%
Therefore, percentage of organs weighs less than 260 grams or more than 440 grams is 5%
(d) What percentage of organs weighs between 215 grams and 440 grams?
For 215 grams, we apply the 3rd rule to confirm
= 3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ
Mean = 350 grams
Standard deviation = 45 grams
μ - 3σ
= 350 - 3(45)
= 350 - 135
= 215.
Hence, 99% of the organs weigh 215 grams
For 440, from the solve questions above, we know the second rule applies.
Hence,
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Mean = 350 grams
Standard deviation = 45 grams
μ + 2σ
= 350 + 2(45)
= 350 + 90
= 440
Hence,
99% + 95%/ 2
= 194% / 2
= 97%
Therefore, about 97% of organs weighs between 215 grams and 440 grams
