Answer:
a) 68% of organs will be between 270 and 370 grams
b) 95%
c) 5%
d) 97.35%
Step-by-step explanation:
Empirical rule states that
1 standard deviation means a 68% of total area under the normal distribution. On one side is half = 34%.
2 standard deviations means a 95% of total area under the normal distribution. On one side is half = 47.5%.
3 standard deviation means a 99.7% of total area under the normal distribution. On one side is half = 49.85%.
a) Since 1 standard deviation means a 68% of total area under the normal distribution, we have
320 + 50 = 370
320 – 50 = 270
68% of organs will be between 270 and 370 grams
b) Calculate the difference between mean and the percentage of weight of an organ in the problem:
420 – 320 = 100
320 – 220 = 100
Since standard deviation is 50 grams, there is a difference of 2 standard deviations for both sides. According to the rule 95% of the organs are between 200 and 420 grams.
c) Since 95% of the organs are between 200 and 420 grams, 5% weighs less than 220 grams or more than 420 grams.
d) Calculate the difference between mean and the percentage of weight of an organ in the problem:
420 – 320 = 100
320 – 170 = 150
Since standard deviation is 50 grams, there is a difference of 2 standard deviations for the right side and 2 standard deviations for the left side. According to the rule for 2 standard deviations on one side there is 47.5% and for 3 standard deviations on one side there is 49.85%. so percentage of organs weighs between 170 grams and 420 grams is 47.5% + 49.85% = 97.35%.
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