When the total population sizeNis known, the confidence interval for an unknown population proportionpcan be used to produce a confidence interval for the total number of population items with a particular characteristic. To estimate the total number of population items with a particular characteristic, multiply the lower and upper confidence limits of the estimate ofpby the population size N. So the confidence interval estimator for the total number of population items with a particular characteristic is

(N*[], N*[])

Companies that advertise their products on television use this technique to estimate the total number of viewers that will see their advertisement. An automaker whose cars appeal to 18- to 49-year-olds would like to place an advertisement on theBig Bang Theorythat airs Thursdays in the 8:00pm to 8:30pm time period.

The decision to place the advertisement will depend on the estimate of the total number of 18- to 49-year-olds that watch theBig Bang Theoryduring the Thursday 8:00pm to 8:30pm time period.

The A. C. Nielsen TV ratings for the 18- to 49-year-old demographic group during a recent Thursday 8:00pm - 8:30pm time period show that, among the 5,000 Nielsen households with a viewer between 18 and 49 years of age, 275 of the households watched theBig Bang Theory. US Census Bureau data indicate that the total number of Americans who are between 18 and 49 years old is 126.54 million.

Denote bypthe proportion of all Americans between 18 and 49 years of age that watchBig Bang Theoryon Thursdays during the 8:00pm to 8:30pm time period.

Question. Determine the 95% confidence interval forpand use the interval forpto construct a 95% confidence interval for the total number of Americans between 18 and 49 years old that watchBig Bang Theoryon Thursdays during the 8:00pm to 8:30pm time period.

Lower limit of 95% confidence interval of all Americans between 18 and 49 years old that watchBig Bang Theoryon Thursdays during the 8:00pm to 8:30pm time period (use 2 decimal places)

Upper limit of 95% confidence interval of all Americans between 18 and 49 years old that watchBig Bang Theoryon Thursdays during the 8:00pm to 8:30pm time period (use 2 decimal places).