Question

The weight of an organ in adult males has a​ bell-shaped distribution with a mean of 310 grams and a standard deviation of 45 grams. Use the empirical rule to determine the following. ​

(a) About 68​% of organs will be between what​ weights? ​

(b) What percentage of organs weighs between 220 grams and 400 ​grams? ​

(c) What percentage of organs weighs less than 220 grams or more than 400 ​grams?

​(d) What percentage of organs weighs between 220 grams and 355 ​grams?

Answer 1

about 68% of observation of data lie within 1 std dev away from mean
about 95% of observation of data lie within 2 std dev away from mean
about 99.7% of observation of data lie within 3 std dev away from mean

a) µ±1σ = (310±45) = (265 , 355)

b)

we need to calculate probability for ,              
P (   220   < X <   400   )
=P( (220-310)/45 < (X-µ)/σ < (400-310)/45 )              
              
P (    -2.000   < Z <    2.000   )

about 95% of observation of data lie within 2 std dev away from mean
answer: 95%

c)

5%  percentage of organs weighs less than 220 grams or more than 400 ​grams

d)

we need to calculate probability for ,                  
P (   220   < X <   355   )  
=P( (220-310)/45 < (X-µ)/σ < (355-310)/45 )                  
                  
P (    -2.000   < Z <    1.000   )   

percentage of organs weighs between 220 grams and 355​grams = (95%/2 + 68%/2) = 81.5%