Question

An unconfined compression test was performed to determine the average strength of concrete cylinders (in psi). It is believed that the strength is approximately normally distributed with a standard deviation of 196 psi. A sample of 50 concrete cylinders was taken, and it was found that the average strength was 2500 psi. Find a 92% confidence interval for the true average strength of the concrete.

Answer 1

Answer:

True average strength in 92% confidence level is 2500±48.5352, that is between 2451.465 and 2548.535

Step-by-step explanation:

Margin of error from the average strength is given by the formula:

z× ($\frac{s}{\sqrt{N} }$) where

• z is the corresponding z-score in 92% confidence level
• s is the standard deviation of the strength of concrete cylinders
• N is the sample size of the compression test

z=1.751 s=196 psi N=50

1.751× ($\frac{196}{\sqrt{50} }$) = 48.5352

Since average strength is 2500 psi, the confidence interval in 92% confidence level is

2500±48.5352