Solution Found!
Radioactive mass A emits particles at a mean rate of 20
Chapter 4, Problem 13E(choose chapter or problem)
Radioactive mass \(A\) emits particles at a mean rate of 20 per minute, and radioactive mass \(B\) emits particles at a mean rate of 25 per minute.
a. What is the probability that fewer than 200 particles are emitted by both masses together in a five-minute time period?
b. What is the probability that mass \(B\) emits more particles than mass \(A\) in a two-minute time period?
Equation Transcription:
Text Transcription:
A
B
Questions & Answers
QUESTION:
Radioactive mass \(A\) emits particles at a mean rate of 20 per minute, and radioactive mass \(B\) emits particles at a mean rate of 25 per minute.
a. What is the probability that fewer than 200 particles are emitted by both masses together in a five-minute time period?
b. What is the probability that mass \(B\) emits more particles than mass \(A\) in a two-minute time period?
Equation Transcription:
Text Transcription:
A
B
ANSWER:Solution
Step 1 of 4
Let X represents the no. of particles emitted by radioactive mass A
Let Y represents the no. of particles emitted by radioactive mass B
a) Here we have to find the probability that fewer than 200 particles are emitted by both A and B together in 5 minutes time period
In 1 minutes time period no. of particles emitted by A is 20
In 5 minutes time period no. of particles emitted by A is 20(5)=100
In 1 minutes time period no. of particles emitted by B is 25
In 5 minutes time period no. of particles emitted by B is 25(5)=125
Here X and Y follows the poisson distribution
XPoisson(100)
YPoisson(125)
Here X follows the normal distribution with mean 100 and standard deviation 100
Here Y follows the normal distribution with mean 125 and standard deviation 125