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.
------------
|
|
|
