Answer:
Explanation:
Given that:
The mean μ = 310
The standard deviation σ = 40
Using the empirical rule to determine the following :
a. About 95 % of organs will be between what weights?
At 95% data values lies within 2 standard deviations of mean.
Thus, the required range is :
= μ ± 2σ
= ( 310 - 2 (40) , 310 + 2(40) )
= (230, 390)
b. What percentage of organs weighs between 270 grams and 350 grams
Here:
μ ± σ = (310 - 40, 310 + 40)
μ ± σ = (270, 350)
Using empirical rule, 68% data values is in the range within 1 standard deviation of mean. This implies that 68% data values lie between (270, 350).
c. What percentage of organs weighs less than 270 grams or more than 350 grams?
The complement theorem can be use to estimate the percentage of organs that weighs less than 270 grams or more than 350 grams,
This can be illustrated as :
= 100 % - 68 %
= 32 %
d. What percentage of organs weighs between 230 grams and 430 grams?
Using the empirical rule:
The percentage of organs weighs between 230 grams and 430 grams is:
u - 2σ and u + 3σ respectively.