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Chapter 5: Q. 66 (page 351)

Carbon-14 is a radioactive element with a half-life of about

5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14.

We are interested in the time (years) it takes to decay carbon-14. In words, define the random variable X.

Short Answer

Expert verified

The value of random variable X is 14 years life of carbon-14

Step by step solution

01

Definition of  the decay rate of carbon-14

The decay rate of carbon-14 is indicated the amount of reducing radioisotope of a carbon-14 per unit time.

02

 The process to measure  the random variable of  carbon-14

On the basis of the information of carbon-14, it exponentially decays with a half-life of 5730 years.

As per this statement, it can be stated that the value of random variable X is 14 years life of carbon-14.

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Most popular questions from this chapter

Carbon-14 is a radioactive element with a half-life of about

5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14.

We are interested in the time (years) it takes to decay carbon-14. The distribution for X is ______.

Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

Find the third quartile of ages of cars in the lot. This means you will have to find the value such that 34or75%,of the cars are at most (less than or equal to) that age.

a. Sketch the graph, and shade the area of interest.

b. Find the value k such thatP(x<K)=0.75

c. The third quartile is _____

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.

According to a study by Dr. John McDougall of his live-in weight loss program, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let鈥檚 suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. a. Define the random variable. X = _________ b. X ~ _________ c. Graph the probability distribution. d. f(x) = _________ e. 渭 = _________ f. 蟽 = _________ g. Find the probability that the individual lost more than ten pounds in a month. h. Suppose it is known that the individual lost more than ten pounds in a month. Find the probability that he lost less than 12 pounds in the month. i. P(7 < x < 13|x > 9) = __________. State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.

The number of days ahead travelers purchase their airline tickets can be modeled by an exponential distribution with the average amount of time equal to 15 days. Find the probability that a traveler will purchase a ticket fewer than ten days in advance. How many days do half of all travelers wait?
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