Probability Question. Normally distributed

[mah062]

1) (1 pt) The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with μ=71 and σ= 8.5 grams per mililiter.

a) What is the probability that the amount of collagen is greater than 65 grams per mililiter?
Answer: 0.761

b) What is the probability that the amount of collagen is less than 84 grams per mililiter?
Answer: 0.937

c) What percentage of compounds formed from the extract of this plant fall within 1σ of μ(Not sure if this is the right symbol but it's supposed to stand for the mean)?
Answer: ?

2) Relevant equations...
P([(x-μ)/σ]<Z<[(x-μ)/σ])

Normally Distributed...
f(x)=[1/(σ√(2pi))][e^(-0.5[(x-μ)/σ]^2)]



3. The Attempt at a Solution .
I've tried everything I can think of. I used P([(62.5-71)/8.5]<Z<[(79.5-71)/8.5]) but it was wrong. I've attempted it 28 different ways. Can anyone help me? Thanks!

 

[Ray Vickson]

1) (1 pt) The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with μ=71 and σ= 8.5 grams per mililiter.

a) What is the probability that the amount of collagen is greater than 65 grams per mililiter?
Answer: 0.761

b) What is the probability that the amount of collagen is less than 84 grams per mililiter?
Answer: 0.937

c) What percentage of compounds formed from the extract of this plant fall within 1σ of μ(Not sure if this is the right symbol but it's supposed to stand for the mean)?
Answer: ?

2) Relevant equations...
P([(x-μ)/σ]<Z<[(x-μ)/σ])

Normally Distributed...
f(x)=[1/(σ√(2pi))][e^(-0.5[(x-μ)/σ]^2)]



3. The Attempt at a Solution .
I've tried everything I can think of. I used P([(62.5-71)/8.5]<Z<[(79.5-71)/8.5]) but it was wrong. I've attempted it 28 different ways. Can anyone help me? Thanks!

In your expression above, where does the number 62.5 come from? Where does the 79.5 come from? Why do you have two inequalities on Z?

RGV