00:01
Hello students, as per the given question, it is given that the sample population standard deviation sigma is equals to 400, confidence level is equals to 95 percent confidence level and the z score for 95 percent confidence level is 1 .96 approximately and sample mean x bar is equals to 270.
00:24
And now we have formulas that we would be using for the next bits where margin of error is equals to z into sigma by root n and the confidence interval is equals to x bar minus margin of error comma x bar plus margin of error.
00:46
So, now let us solve the bit a first where it is given that n is equals to 25 and the rest of the values are same where z and sigma and x bar values are same.
00:58
So, let us calculate the margin of error for bit a where it is given as 1 .96 into 40 divided by root 25.
01:10
This value gives 15 .68 as the margin of error and the confidence interval is equals to after substituting the values in this above equation it gives the value as 270 minus 15 .68 comma 270 plus 15 .68 which is equals to 254 .32 comma 285 .68.
01:43
Now, let us solve for bit b where given that n is equals to 50 and it is let us substitute these values in the margin of error formula which gives the equation as 1 .96 into 40 divided by root 50 which is equals to 11 .31 as the answer and the confidence interval is equals to after substituting these values in the above confidence interval formula which gives the answer as 270 minus 11 .31 comma 270 plus 11 .31 which gives the answer as 258 .69 comma 281 .31.
02:30
And now coming to the bit c where n is given as 100.
02:35
So, the sample we need to substitute the sample size in the equation of m e...