1. 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 225 psi. A sample of 60 concrete cylinders was taken, and it was found that the average strength was 2600 psi. Find a 93% confidence interval for the true average strength of the concrete.

So on this case the 93% confidence interval would be given by (2547.424;2652.576)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean

population mean (variable of interest)

represent the population standard deviation

n =60represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

Since the Confidence is 0.93 or 93%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.035,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 93% confidence interval would be given by (2547.424;2652.576)