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A store sells a large number of packets of resistors. They are packed in $3$ packet sizes: $10$,$20$ and $30$ resistors per packet and are sold int the ratio $1:3:2$ respectively. A random sample of $3$ packets is taken from the shelve.

(i) List the sample space.

(ii) Determine the sampling distribution of the mean and median.

What i tried

(i)The sample space represents all the possible outcomes of the resistors being chosen which in this case are all the possible combinations of the resistors per packet chosen. But i dont quite get what has the ration $1:3:2$ has go anything to do with this . Could anyone pleas explain. Thanks

(ii) The mean is $(10*1+20*3+30*2)/(1+3+2)$ to get the average number of resistors per packet. The median is the $50th$ percentile which is $20$ resistors per packet. Am i correct. Could anyone explain. Thanks

ys wong
  • 2,017
  • The sample space is the set of all possible sets of three choices e.g. one outcome is (1, 1, 1), meaning three of the first size pack are chosen. The ratios given have no role in writing down the sample space. They do however dictate the probability of each outcome in the sample space. – Paul Apr 25 '17 at 15:56
  • So the should be a total of $3*3=9$ outcomes? Then how about part(ii)? – ys wong Apr 25 '17 at 16:05
  • 9 outcomes yes as the number sold is large. The mean number of resistors is the expected sum of the three chosen packets, which is the sum of the resistors for that outcome multiplied by the probability of that outcome (9 such products), which are then added together. The probability of each outcome can be done assuming independence. – Paul Apr 25 '17 at 16:29

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