A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a

Mathematics

1 answer:

8_murik_8 [283]2 years ago

7 0

Answer:

We are given

Scientist begins with 150 milligrams of a radioactive substance

so,

we can use formula

we can plug Po=150

After 29 hours, 75 mg of the substance remains

so, at t=29 , P=75

we can plug it

now, we can solve for k

now, we can take ln on both sides

now, we can plug it back

and we get

we can plug t=33

we get

..............Answer

Step-by-step explanation:

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .