A factory manufactures precision-calibrated weights for laboratory use. They produce two standard masses: Type A and Type B. The weight of a Type A mass, XXX g, follows the distribution N(12.50,0.082)N(12.50, 0.08^2)N(12.50,0.082). The weight of a Type B mass, YYY g, follows the distribution N(24.20,0.122)N(24.20, 0.12^2)N(24.20,0.122). A random sample of 3 Type A masses and 5 Type B masses is selected for quality control testing.
Find the probability that the combined weight of these 8 masses is greater than 159.0 g.
A random sample of 2 Type B masses is selected.
Find the probability that the difference between the weights of these 2 Type B masses is more than 0.15 g.
A random sample of n+1n+1n+1 Type A masses is taken, with weights X1,X2,X3,…,Xn+1X_1, X_2, X_3, \dots, X_{n+1}X1,X2,X3,…,Xn+1. The random variable TTT is defined as
T=nX1−∑r=2n+1Xr T = n X_1 - \sum_{r=2}^{n+1} X_r T=nX1−r=2∑n+1XrGiven that P(T>8.1)=0.0062P(T > 8.1) = 0.0062P(T>8.1)=0.0062 to 4 decimal places,
calculate the value of nnn.