For each of the following experiments, decide whether it would be appropriate to
ID: 3204693 • Letter: F
Question
For each of the following experiments, decide whether it would be appropriate to use a sample space which is finite, countably infinite, or continuous. (a) A Geiger counter, located adjacent to a building containing a reactor, will record the total number of alpha particles during a one-hour period. (b) Five of the members of a professional society with 12, 600 members are chosen to serve on a nominating committee. (c) An experiment is conducted to measure the thickness of a new synthetic silk thread in nanometers. (d) A study is made to determine in how many of 450 airplane accidents the main cause is pilot error. (e) Measurements are made to determine the uranium content of a certain ore. (f) In a torture test, a watch is dropped a number of times from a tall building until it stops running.Explanation / Answer
To determine whether given experiment has finite or countably infinite or continuous sample space, we need to check underlying variable.
a) Number of alpha particles emitting during one hour period can be 0, 1, 2 …… etc. Therefore it would be appropriate to use Countably infinite sample space for this experiment.
b) Choosing 5 members to serve on nominating committee out of 12600 members has finite choices. Hence it would be appropriate to use Finite sample space for this experiment.
c) Thickness of silk thread would be measured in nanometres units and hence it would be appropriate to use Continuous sample space for this experiment.
d) Number of airplane accidents for which main cause is pilot error can be 0, 1, 2…. 450. Hence it would be appropriate to use Finite sample space for this experiment.
e) The uranium content in an ore can be measured in tonnes. Hence it would be appropriate to use Continuous sample space for this experiment.
f) Number of times a watch can be dropped until it stops running can be 0, 1, 2 …… etc. Therefore it would be appropriate to use Countably infinite sample space for this experiment.
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