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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.

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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× ([tex]\frac{s}{\sqrt{N} }[/tex]) 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× ([tex]\frac{196}{\sqrt{50} }[/tex]) = 48.5352

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

2500±48.5352