Problem
Two distinct solid fuel propellants, type A and Type B, are being considered for a space program activity. From past data we know that the standard deviation of burning rate of two propellants are the same and equal to 5 cm/sec and the means of the burning rate for propellant A and propellant B equal 20.5 cm/sec and 22.5 cm/sec, respectively. Random samples of 21 specimens of each propellant are taken.
(a) What is the probability that the mean of the burning rate of sample of propellant A is between 19 cm/sec and 22 cm/sec?
(b) What is the probability that the difference between two sample means of burning rates is less than 0.5?
(c) What is the probability that the ratio S2
1=S2
2 is less than 2.124, where S2
1 and S2
2 are sample variances
of the burning rate of specimens of propellant A and B, respectively?
(d) If we assume that the variance of the burning rate of propellant A, i.e. 21 is unknown and the corresponding sample variance equals 36 cm2=sec2 ; what is the probability that the sample mean of the burring rate of propellant A exceed 23.80993?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.