 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, find 95% confidence interval for the population proportion for a sample size of 120 and sample proportion 0.7. Before starting the solution of this question we should know a result that is to find range of population proportion given by P for 95% confidence interval we use the following formula which is P cap minus of 2 into square root of P cap into 1 minus P cap the whole upon N is less than P which is less than P cap plus 2 into square root of P cap into 1 minus P cap the whole upon N where P is the population proportion and P cap is the sample proportion also N denotes the size of the sample with this key idea we shall proceed to the solution. Now in this question we have to find 95% confidence interval for population proportion and we are given sample size which is denoted by N as 120 that is sample size which is denoted by N is given to us as 120 and sample mean that is sample proportion is given to us as 0.7 sample proportion which is denoted by P cap is given to us as 0.7 let P be the population proportion then from the key idea we know that the 95% confidence interval are given by P cap minus 2 into square root of P cap into 1 minus P cap the whole upon N is less than P which is less than P cap plus 2 into square root of P cap into 1 minus P cap the whole upon N where P is the population proportion P cap is the sample proportion and N denotes size of sample so on putting the values of P cap and N in this we get 0.7 minus of 2 into square root of 0.7 into 1 minus 0.7 the whole upon 120 is less than P is less than 0.7 plus 2 into square root of 0.7 into 1 minus 0.7 the whole upon 120 which implies that 0.7 minus of 2 into square root of 0.7 into 1 minus 0.7 that is 0.3 whole upon 120 is less than P is less than 0.7 plus 2 into square root of 0.7 into 1 minus 0.7 that is 0.3 whole upon 120 and this further implies that 0.7 minus of 2 into square root of 0.7 into 0.3 that is 0.21 upon 120 is less than P is less than 0.7 plus 2 into square root of 0.7 into 0.3 that is 0.21 upon 120 which further implies that 0.7 minus of 2 into square root of 0.21 upon 120 which is given by square root of 0.00175 is less than P is less than 0.7 plus 2 into square root of 0.21 upon 120 that is square root of 0.00175 which implies that 0.7 minus 2 into square root of 0.00175 that is 0.041 is less than P is less than 0.7 plus 2 into square root of 0.00175 that is 0.041 this further implies that 0.7 minus of 2 into 0.041 that is 0.082 is less than P is less than 0.7 plus 2 into 0.041 that is 0.082 and this further implies that 0.7 minus of 0.082 that is 0.618 is less than P is less than 0.7 plus 0.082 that is 0.782 thus the confidence interval is the open interval from 0.618 to 0.782 so true value of population proportion will lie in this interval which is the required answer this completes our session hope you enjoyed this session