Determine the number of 1000 different confidence intervals would contain the true value of the population mean.

The number of 1000 different confidence intervals would contain the true value of the population mean with the confidence level of 96% is obtained below as follows:

From the information, given that there are 1000 different random samples was selected from the same population.

The required number is,

\(\displaystyle{1000}\times{\frac{{P}}{{96}}}\rbrace{\left\lbrace{100}\right\rbrace}={960}\)

Thus, on average 960 of 1000 different confidence intervals would contain the true value of the population mean with the confidence level of 96%.

Step 2

Determine the number of 1000 different confidence intervals would contain the true value of the population mean.

The number of 1000 different confidence intervals would contain the true value of the population mean with the confidence level of 99% is obtained below as follows:

From the information, given that there are 1000 different random samples was selected from the same population.

The required number is,

\(\displaystyle{1000}\times{\frac{{{99}}}{{{100}}}}={990}\)

Thus, on average 990 of 1000 different confidence intervals would contain the true value of the population mean with the confidence level of 99%.