Problem solving with inequalities
1 answer:
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Answer:
a) 99.7%
b) 68%
c) 68% of organs weighs between 275 and 365 grams, so 32% of organs weighs will be less than 275 or more than 365 grams.
d) 81.5% of organs weighs between 290 grams and 365 grams.
Step-by-step explanation:
A) 99.7% of organs will be between 3 standard deviation from the mean.
So 99.7% of organs will be between 185 and 455.
B) 275 grams and 365 grams are 1 standard deviation from the mean.
From empirical rule about 68% data falls within 1 standard deviation from the mean.
So 68% of organs weighs btwn 275 grams and 365 grams.
C) Since 68% of organs weighs between 275 and 365 grams, so 32% of organs weighs will be less than 275 or more than 365 grams.
D) 230 is 2 standard deviation below the mean and 365 is one standard deviation above the mean.
According to the empirical rule, 95% of the observation lies within 2 standard deviations of the mean. Therefore 5% lies outside 2 standard deviations of the mean.
So 95%/2 = 47.5% of organs weighs between the mean and 230 grams.
According to the empirical rule about 68% data falls within one standard deviation from the mean.
so, 68%/2 = 34% of organs weighs between the mean and 365 grams.
So total = 47.5% + 34% = 81.5% of organs weighs between 290 grams and 365 grams.