00:01
In this question, we are given name is equal to 510 .88.
00:07
Standard variance is equal to 15, 326.
00:12
5 .3.
00:14
Therefore, standard deviation or s is equal to root over variance, which is equal to 123 .8.
00:26
Now, also we are given n is equal to 60.
00:30
Then the first question you need to calculate standard error of mean.
00:39
Standard error of minimum formula is equal to standard deviation over root n.
00:44
Standard deviation we already have 123 .8 over root n is 65.
00:51
Therefore standard error is equal 15 .535 or 15 .36.
01:00
Therefore we are the first question that is standard.
01:02
Error is equal to 15 .36 is the answer for the first part.
01:07
Second part we need to calculate fraction of sample that lies below 490.
01:16
So we can also write this as p x bar minus mu over standard deviation over written it is standard error less than 490 minus mu which is given us 510 minus 88 devoured by standard error which is 15 .36 so our z score for this is p z less than so if we solve the right hand side we get z value is minus 1 .359 now this is left and this is a left tail test so from z table or the standard normal table or the standard normal table table we can get the value of z the value for z less than minus 1 .3 is equal to 0 .07 therefore we can write that the fraction of fraction of sample that lies below 419 a 0 .087 is the answer for the second part.
02:45
Now the third part, we need to calculate fraction of the sample that will fall within 20 or some of the population means.
02:54
So let our population mean is 0.
02:57
So again, we'll calculate the z score of this...