Problem 20SE

The answer to Exercise 19 part (d) is needed for this exercise. A geologist counts 64 emitted particles in one minute from a certain radioactive rock.

a. Find a 95% confidence interval for the rate of emissions in units of particles per minute.

b. After four minutes, 256 particles are counted. Find a 95% confidence interval for the rate of emissions in units of particles per minute.

c. For how many minutes should errors be counted in order that the 95% confidence interval specifies the rate to within ± 1 particle per minute?

Step 1 of 3</p>

a) The no. of emitted particles counted by geologist is 64

Here we have to find the 95% confidence intervals

The 95% confidence intervals are

is the critical value at 5% level of significance

Then =1.96

Here X=64, n=1, =64

Then 1.96 = 64

=(48.62, 79.68)

Hence the 95% confidence intervals are (48.62, 79.68)

Step 2 of 3</p>

b) 256 particles emitted in 4 minutes

The 95% confidence intervals are

is the critical value at 5% level of significance

Then =1.96

Here X=256, n=4

=256/4

=64

The 95% confidence intervals are =

=

=(56.14, 71.84)

Hence the 95% confidence intervals are (56.14, 71.84)