Download STAT 495, Fall 2003 Homework Assignment #9

STAT 495, Fall 2003
Homework Assignment #9
1. A company uses mechanical switches in one of its products. The company wants the
switches to withstand 50,000 on/off cycles without failure. A new supplier ships 200
switches for inspection and testing by the the company. Assume that 30 of the 200
switches will fail before they reach 50,000 cycles. If ten switches are chosen at random
and put on test, what is the chance that none of the ten will fail before they reach
50,000 cycles? one will fail? two will fail ? half will fail? Since the ten switches are
put on test at the same time, sampling is done without replacement.
2. At home you have a drawer full of batteries. Some of them are good, will light the single
battery flashlight, and some are bad, will not light the single battery flashlight. Good
and bad batteries are mixed together (you just can’t bring yourself to throw those old
batteries out but you keep buying new ones). Assume that 85% of the batteries are
good and 15% of the batteries are bad. You sample batteries from the drawer with
replacement, that is you choose a battery, check to see if it is good or bad and throw
it back into the drawer. Why you are doing this is not obvious but could be related
to taking a statistics course during the fall semester. If you sample ten batteries at
random with replacement, what is the chance that all ten will be good? one will be
bad? two will be bad? half will be bad?
3. What are the similarities and differences between the set up of problems 1 and 2? How
close are the probabilities calculated in 1 and 2? Which probabilities were easier to
calculate? What does this illustrate about the difference between the binomial and
hypergeometric probability distributions when you sample 10 items from an original
population with and without replacement?
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