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?
(a) 
confidence interval for ? is therefore 64 ± 1.96(8), or (48.32, 79.68).
(b) 
confidence interval for ? is therefore 64 ± 1.96(4), or (56.16, 71.84).
(c) Let n be the required number of minutes. Then n satisfies the equation 
. Substituting 
for ? and solving for n yields n = 245.86 minutes.
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