Chapter 5: Q. 71 (page 352)

Thirty percent (30%) of carbon-14 will decay within how many years?
a. Sketch the graph, and shade the area of interest.
b. Find the value k such that P(x < k) = 0.30.

Short Answer

Expert verified

The graph, and shade of the interest area has been provided in step 1

the value of the probability $P (x < k) = 0.30$ is $2, 947.93$

Step by step solution

Function of probability distribution

It has been given that

$X ~ E x p (0.000121)$

So, the mean value m = $0.000121$

the formula of probability density is

At x= $0$ the value of $f (x)$ lies in Y axis then value of

$\begin{array}{rcl} f (x) & = & 0.000121 e^{- 0.000121 \times 0} \\ = & 0.000121 \end{array}$

that is equal to mean value of m.

The figure has been provided $P (x < k) = 0.30$

Formula of cumulative distribution

$P (X < x) = 1 - e^{m x}$

m = $0.000121$

Now to calculate 30 percentile, the equation is

$P (x < k) = 1 - e^{0.000121 k} 0.30 = 1 - e^{0.000121 k} e^{0.000121 k} = 0.70$

Applying logarithm in both sides

$\ln (e^{0.000121 k}) = \ln (0.70) k = \frac{0.3567}{0.000121} = 2947.93$

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Thirty percent (30%) of carbon-14 will decay within how many years?
a. Sketch the graph, and shade the area of interest.
b. Find the value k such that P(x < k) = 0.30.

Short Answer

Step by step solution

Function of probability distribution

Formula of cumulative distribution

One App. One Place for Learning.

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Study anywhere. Anytime. Across all devices.

Thirty percent (30%) of carbon-14 will decay within how many years?a. Sketch the graph, and shade the area of interest.b. Find the value k such that P(x < k) = 0.30.

Short Answer

Step by step solution

Function of probability distribution

Formula of cumulative distribution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Thirty percent (30%) of carbon-14 will decay within how many years?
a. Sketch the graph, and shade the area of interest.
b. Find the value k such that P(x < k) = 0.30.