Question

The weight of an organ in adult male has a bell shaped distribution with a mean of 320 grams and a standard deviation of 25 grams. Use the empirical rule to determine the following.A) about 95% of organs will be between what weight?B) what percentage of organs weighs between 295 grams and 345 grams?C) what percentage of organs weigh less than 295 grams or more than 345 grams? D) what percentage of organs weighs between 270 grams and 395 grams? A) ___ and __ grams B) ___%C) ___%D) ___%

Answer 1

From the statement we know that the weight of an organ in an adult male has a bell-shaped distribution with:

• mean μ = 320 g,

,

• standard deviation σ = 25 g.

Answers to the questions

A) From probability theory, we know that 95.45% of the values of a bell-shaped distribution are contained in the interval:

`(\mu-\sigma,\mu+\sigma)=(320g-25g,320g+25g)=(295g,345g)\text{.}`

So about 95% of organs will be between the weights 295g and 345g.

B) Using the last answer, we know that 95.45% of the organs weights between 295g and 345g.

C) From probability theory, we know that values less than x1 = μ - σ or great that x2 = μ + σ represent a 4.6% of the values of a bell-shaped distribution. In this case x1 = μ - σ = 295g and x2 = μ + σ = 345g, so the organs that weigh less than 295g or great than 345g are a percentage of 4.6%.

D) Using the following graph:

We see that:

• values x < μ - 2σ = 320g - 2*25g = 270g represent a 2.1% of the values of the distribution,

,

• values x > μ + 3σ = 320g + 3*25g = 395g represent a 0.1% of the values of the distribution.

So the values in the interval of weighs 270g to 395 represent a 100% - 2.1% - 0.1% = 97.8% of the values of the distribution.

Answers

A) 295 grams and 345 grams

B) 95.45%, or 95.5% to one decimal

C) 4.6%

D) 97.8%

.