Problem 18E

You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a refund. Let X be the number of decay events counted in 10 seconds.

a. If the mean decay rate is exactly 1 per second (so that the claim is true, but just barely), what is P(X ≤ 1)?

b. Based on the answer to part (a), if the mean decay rate is 1 particle per second, would one event in 10 seconds be an unusually small number?

c. If you counted one decay event in 10 seconds, would this be convincing evidence that the product should be returned? Explain.

d. If the mean decay rate is exactly 1 per second, what is P(X ≤ 8)?

e. Based on the answer to part (d), if the mean decay rate is 1 particle per second, would eight events in 10 seconds be an unusually small number?

f. if you counted eight decay events in 10 seconds would this be convincing evidence that the product should be returned? Explain.

Step 1 of 7</p>

Let X be the No. of decay events counted in 10 seconds

Here XPoisson(10)

The pmf of poisson distribution is P(x)=, x=0,1,2,.......

Step 2 of 7</p>

a)We have to find P(x1) if the mean decay rate is exactly 1 per second

Now P(x1)=P(0)+P(1)

=+

=0.000045+0.00045

=0.0005

if the mean decay rate is exactly 1 per second P(x1)=0.0005

Step 3 of 7</p>

b) Yes , if the mean decay rate is exactly 1 per second

one event in 10 seconds is unusually a small number

Because it occurs once in 2000 cases

Step 4 of 7</p>

c) Yes, this is the convincing evidence that the product should be returned

Because the probability is only 0.0005

And if the mean decay rate is exactly 1 per second

one event in 10 seconds is unusually a small number