2. (10 points) Two distinct solid fuel propellants, type A and type B, are being

Question

2. (10 points) Two distinct solid fuel propellants, type A and type B, are being considered for a space program activity. Burning rate of the propellant are crucial. Random samples of 20 specimens of the two propellants are taken. It is generally assumed that the variability in burning rate is roughly the same for the two propellants and is given by a population standard deviation of 5 cm/sec. Assume that the burning rates for each propellant are approximately normal and hence make use of the Central Limit Theorem. If, indeed, the population means of the two propellants are equal, what is the probability that the sample mean of propellant B exceeds the sample mean of propellant A by at least 4 cm/sec.?

Explanation / Answer

Here population standard deviation = 5 cm/sec

Here population mean are equal but we have to find the probability that the sample mean of propellant B exceeds the sample mean of propellant A by at least 4 cm/sec. where is same for each type of propleents.

Pr(x1 - x2 > 4  ; ; 5) = ?

standard error of proportion difference = sqrt [s12 /n1 + s22 /n2 ] = sqrt [52 /20 + 52 /20] = 1.5811

so Here Z = (4 - 0)/ 1.5811 = 2.53

Pr(x1 - x2 > 4  ; ; 5) = Pr (Z > 2.53) = 1 - 0.9943 = 0.0057

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