A sample of a radioactive isotope had an initial mass of 550 mg in the year 2009 and decays exponentially over time. A measurement in the year 2015 found that the
sample's mass had decayed to 90 mg. What would be the expected mass of the
sample in the year 2020, to the nearest whole number?

it has the same slope and a different y-intercept

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question 1: step-by-step explanation:

1/4 of 84 = 84÷4= 21

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.

answer: c

step-by-step explanation