Question 1048931: Is there an answer for the following posted, I'm trying to help a student but i need a solved reference (in the interest of time I work a lot) i can't find a solved version anywhere
Park Rangers in Yellowstone Park have found fawns < 6 months old have an approximate body weight normally distributed with a mean =26.1 kg and a standard deviation =4.2 kg x is the weight of fawns in kg
Rewrite each of the following word problems into a probability expression.ex P(x>30)
convert each expression involving x into a probability expressioninvolving z using the scenario
sketch a normal curve for each z with appropriate shading
solve
probability of selecting a fawn less than 6 months old that weighs less than 25kg?
probability of selecting a fawn less than 6 months old that weighs more than 19kg?
probability of selecting a fawn less than 6 months old that weighs 30-38 kg?
if less than 6 months old weighs 16 pounds is it unusually small ?explain/verify mathematically
what is the weight less than 6 months old that is a 20% probability of being randomly selected ?
explain and verify mathematically
thank you all
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Prob fawn <25 kg
z=(x-26.1)/4.2
=-1.1/4.2=-0.262
Probability z=-0.262=0.3967 Shade the area to the left of -0.262
Probability (wt>19 kg)
z=(19-26.1/4.2)=-1.6667
Shade the area to the right, and that is 0.9522
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Need z for 30 and for 38
for 30
(30-26.1/4.2)=0.9286
for 38
(38-26.1)/4.2=11.9/4.2=2.8333
The z in that range corresponds to a probability of 0.1742. Shade between the z values
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fewer than 16 lb or 16/2.2=7.3 kg
z=(7.3-26.1)/4.2=--18.8/4.2=-4.48
probability (shade to the left of -4.48) is 0. If they meant 16 kg, and not 16 pounds, by the same approach it would be 0.008. That would still be highly unlikely.
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No one exact weight has a 20% chance of being randomly selected. A range has a 20% chance.
The 20th percentile is a z=-0.84
-0.84=(x-mean)/4.2
-3.528=x-mean
x=26.1-3.5=22.6 kg
The probability of selecting a fawn with weight <22.6 kg is 20%. That is to the left of the z=-0.84 part of the curve.
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