SOLUTION: The amount of caffeine in an 8 oz. energy drink is approximately normally distributed with a mean of 101 mg. and a standard deviation of 37.4 mg. Determine:
a) The proportion (per
Algebra.Com
Question 1041210: The amount of caffeine in an 8 oz. energy drink is approximately normally distributed with a mean of 101 mg. and a standard deviation of 37.4 mg. Determine:
a) The proportion (percentage) of 8oz. energy drinks that are expected to contain less than 71 mg. of caffeine.
b) The proportion (percentage) of 8 oz. energy drinks that are expected to contain between 65 and 125mg. of caffeine
c) The percent of 8 oz. energy drinks that are expected to contain greater than 150 mg. of caffeine
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The amount of caffeine in an 8 oz. energy drink is approximately normally distributed with a mean of 101 mg. and a standard deviation of 37.4 mg. Determine:
a) The proportion (percentage) of 8oz. energy drinks that are expected to contain less than 71 mg. of caffeine.
z(71) = (71-101)/37.4 = -0.8021
p(x < 71mg) = p(z < -0.8021) = normalcdf(-100,-0.8021) = 0.2112 = 21.12%
------------------------------------------------
b) The proportion (percentage) of 8 oz. energy drinks that are expected to contain between 65 and 125mg. of caffeine
Find the z-value of 65 and or 125.
Ans: normalcdf(65,125,101,37.4) = 57.16%
-----------------------------------
Find the probability of z lying between those two z values.
c) The percent of 8 oz. energy drinks that are expected to contain greater than 150 mg. of caffeine
Find the z-value of 150
Find the probability of z being greater than that z-value.
Ans:: normalcdf(150,1000,101,37.4) = 9.5%
============
Cheers,
Stan H.
------------
RELATED QUESTIONS
One 8-oz serving each of coffee, energy drink, and soda contains 201 (answered by josgarithmetic)
A person drinks Red Rhino energy drink that has approximately 100 mg of caffeine in it.... (answered by ikleyn)
The half-life of caffeine is approximately 5.7 hours and a shot of 5-hour Energy contains (answered by ankor@dixie-net.com)
Ethan consumes an energy drink that has 240 mg of caffeine in it and the caffeine leaves... (answered by josgarithmetic)
Miguel consumes an energy drink that has 200 mg of caffeine in it and the caffeine leaves (answered by josmiceli)
Considering an 8 oz serving size, 1 serving each of brewed coffee, Red Bull energy drink... (answered by josgarithmetic)
The amount of coffee that a filling machine puts into an 8 oz. jar is normally... (answered by stanbon)
Jason's body metabolizes caffeine at a rate of 14.9% per hour (so the amount of caffeine... (answered by Boreal)
Brayden's body metabolizes caffeine at a rate of 13.7% per hour (so the amount of... (answered by josgarithmetic)