Acertain drug dosage calls for 460 mg per kg per day and is divided into four doses (1 every 6 hours). if a person weighs 229 pounds, how many milligrams of the drug should he receive every 6 hours?

11.95 g / 6 hours  

Step-by-step explanation:

drug dosage = 460 mg per kg per day

to be administered every 6 hours to a person who weighs 229 pounds

1 pound = 0.453592 kg

229 pounds = 229 × 1 pound = 229 × 0.453592 kg = 103.873 kg

dosage of drug needed for 103.873 kg

460 mg is to 1 kg per day

103.873 kg = 103.873 × 460 mg per 1 kg per day = 47781.58 mg per 103.873 kg per day

number of 6 hours in a day = 24 hours ÷ 6 hours = 4 times per day

dosage needed per 6 hours

47781.58 ÷ 4 = 11945.395 mg for every 6 hours = 11.95 g / 6 hours  

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.