Assume the amount of caffeine extracted from 8 fluid ounces of coffee brewed in a drip machine is normally distributed. On average, 100 mg of caffeine is extracted with a standard deviation of 10 mg. What is the probability of extracting more than 120 mg of caffeine from 8 fluid ounces of coffee brewed in a drip machine

2.3%

Step-by-step explanation:

Imagine a standard normal curve with mean at 100 mg.  One standard deviation above the mean would be 110 mg; two standard deviations 120 mg.

Draw a vertical line through x = 120.  To answer this question, we must find the area under the curve to the left of x = 120 and then subtract this result from 1.00:  

Using a calculator with probability distribution functions built in, we find the area to the left of x = 120 as follows:  

normcdf(-100,120,100,10)  = 0.977 => 1.000 - 0.977 = 0.023

The probability of extracting more than 120 mg of caffeine from 8 fluid ounces of coffee brewed in a drip machine is 2.3%

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: