Question

4) You are designing an experiment to determine the effect of temperature, stirring rate, and chemical substrates on the yield of a certain process. There are five different temperatures, two different stirring rates, and four different substrates. If each run of the experiment consists ofpicking one temperature, one stiring rate, and two substrates, how many different runs are possible? (Solve with appropriate math, not brute force). How many experimental runs would you recommend conducting in order to perfom statistical analyses on the data? ) In how many different ways can a laboratory technician choose six out of twenty-four mice, inject three of them with a low level of medicine, and the other three of them witha higher dose of medicine? 6.) A system contains two components, A and B. The system will function so long as either A or B functions. The probability that A functions is 0.95. What is the required probability of failure for B if I want to ensure that the systern functions 99.9% of the time.

Answer 1

(4)

Let temperature = T, Stirring rate = S, Chemical substrate = C

There are 5 T's, 2 S's and 4 C's to choose from

We need to choose 1 T, 1 S and 2 C

The selections can happen in C(5, 1) ways, C(2, 1) ways and C(4, 2) ways respectively

Number of runs possible = C(5, 1) * C(2, 1) * C(4, 2) = 5 * 2 * 6 = 60

For further statistical analysis, at least 30 runs are recommended.