Solved Problems

The compressive strength of a certain type of concrete is known to have a mean of 4000 psi and a standard deviation of 500 psi. A random sample of 36 specimens is taken. What is the probability that the average strength of this sample is greater than 4100 psi?

A manufacturer claims that 5% of their bolts are defective. If a civil engineer purchases a random sample of 400 bolts, what is the probability that more than 7% of them are defective?

A machine filling bags of cement has a known variance in weight of $\sigma^2 = 0.25$ kg$^2$. A quality control engineer takes a random sample of $n = 15$ bags and calculates the sample variance $s^2$. Assuming the weights are normally distributed, what is the probability that the sample variance exceeds $0.40$ kg$^2$?