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.
The value of random variable X is 14 years life of carbon-14
The decay rate of carbon-14 is indicated the amount of reducing radioisotope of a carbon-14 per unit time.
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.
The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from to years.
We randomly select one first grader from the class.
a. Define the random variable. = _________
c. Graph the probability distribution.
d. = _________
f. = _________
g. Find the probability that she is over years old.
h. Find the probability that she is between four and six years old.
i. Find the percentile for the age of first graders on September 1 at Garden Elementary School.
Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution:
State the probability density function.
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’s 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. μ = _________ f. σ = _________ 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.
Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks).
a. X ~ _________
b. Graph the probability distribution.
c. f(x) = _________
d. ì = _________
e. ó = _________
f. Find the probability that a person is born at the exact moment week 19 starts. That is, find P(x = 19) = _________
g. P(2 < x < 31) = _________
h. Find the probability that a person is born after week 40.
i. P(12 < x|x < 28) = _________
j. Find the 70th percentile.
k. Find the minimum for the upper quarter
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