Bell-Shaped Distribution (Statistics)?

[iCake]

I'm having difficulties understanding this, I got this all wrong on my test and would like to know how to solve it. Any help is greatly appreciated! Thanks.

The weight of an organ in adult males has a bell-shaped distribution with a mean of 340 grams and a standard deviation of 20 grams. Use the empirical rule to determine to following.

A) About 68% of organs will be between what weights?
340 +/- 20 --> 340+20 = 260 and 340 - 20 = 320
My answer was 260 and 320 grams, but I got it wrong.

B) What percentage of organs weights between 300 AND 380 grams?
300 - 340 = -40%
380 - 340 = 40%
My answer was 80%.

C) What percentage of organs weights less than 300 grams OR more than 380 grams?

My answer was 62.5%. Again, I got it wrong.

D) What percentage of organs weights between 290 AND 440 grams?
280 - 340 = -60
380 - 340 = 40
100% was my answer.

[BeeFree]

iCake

A) About 68% of organs will be between what weights?
340 +/- 20 --> 340+20 = 260 and 340 - 20 = 320
My answer was 260 and 320 grams, but I got it wrong.

Just a math error ...

340+20 = 360 [not 260]

ANSWER: 320 to 360



B) What percentage of organs weights between 300 AND 380 grams?
300 - 340 = -40%
380 - 340 = 40%
My answer was 80%.

40% is 40/20 = 2 standard deviations

Empirical rule says 95% are between 2 standard deviations

ANSWER: 95%



C) What percentage of organs weights less than 300 grams OR more than 380 grams?
My answer was 62.5%. Again, I got it wrong.

Use the answer from (B) above ...

percentage of organs weights less than 300 grams OR more than 380 grams = 100% - 95% = 5%

ANSWER: 5%



D) What percentage of organs weights between 290 AND 440 grams?
280 - 340 = 60
380 - 340 = 40
100% was my answer.


60 is 60/20 = 3 standard deviations

40 is 40/20 = 2 standard deviations

Empirical Rule says 95% and 99.7% are between 2 and 3 standard deviations, respectively.

Here one range is 2 and the other is 3 standard deviations, so average the results ...

(95 + 99.7)/2 = 97.35%

ANSWER: 97.35%

hope that helped

[Elizabethm]

A) 340+20=360 not 260.
B)Z= (300-340)/20=-2 and Z=(380-340)/20=2 giving about 95%
C) 100%-95%=5%
D) Z=-60/20=-3 and Z=40/20=2. P(-3<Z<2)= 97.5%-0.135% ~97%