In a certain survey of the work of chemical research workers, it was found, on the basis of extensive data, that on avegare each man required no fume cupboard for 60% of his/her time, one cupboard for 30% and two cupboards for 10%; three or more were never required. If a group of four chemists worked independently of one another, how many fume cupboards should be available in order to provide adequate facilities for at least 95% of the time?

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Margaret Plemons · Accepted Answer

Step 1 Let the number of fume cupboard required per person be x Then, according to Question. x=0x=1x=2P(x=0)=0.60P(x=1)=0.30P(x=2)=0.10 Determine the expected value of x to determine the number of fume cupboards required on average for one chemist. E(x)=∑xP(x) =0(0.60)+1(0.30)+2(0.10) =0.30+0.20 =0.50 Therefore, average number of number of fume cupboards required per person is 0.50. Step 2 Total number of chemist working are 4. Therefore, determine the number of fume cupboards required on average for four chemist. Average=4×0.5 =2 Now, the number of fume cupboards required in order to provide adequate facility for 4 chemists at least 95% of the time. Determine the 95% of average time. Number of fume cupboard=95%×2 =95100×2 =0.95×2 =1.9 Therefore, the number of fume cupboards required in order to provide adequate facility for 4 chemists at least 95% of the time are 1.9.

In a certain survey of the work of chemical research workers, it was f

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