2. You want to test the strength of a certain type of steel cable, which should

Question

2. You want to test the strength of a certain type of steel cable, which should satisfy the standard of: the mean is 400 psi, with the standard deviation 50 psi. Assume that the quality of the cable is up to the standard and follows a normal distribution. From a sample of n=64 cables, what is the probability that the value of your calculated sample mean is a) between 388 and 406 psi; b) above 415 psi. 3. To find out the real (population) mean of a type of battery's hours, you took a sample of n=6 and got the following data: 2.6, 3.6, 2.5, 3.3, 2.9, and 3.1 hours. a) Compute the Sample Mean and the Sample Variance. b) What is your two-sided 95% confidence interval for the real population mean?

Explanation / Answer

Mean =400 psi, std dev = 50 psi

Given this follows a normal distribution.

n =64, Hence std error = 50/rt 64 = 6.25

Z score for 388 = -12/6.25 = -1.92

z score for 406 = 2.88

z score for 415 = 2.4

a) P(388<x<406) = P(-1.92<z<2.88) = 0.4726+0.4979 = 0.9705

b) P(x>415) = P(z>2.4) = 0.5-0.4918 = 0.0082

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