00:01
Hello students, let's do this question.
00:02
In this question, sample of x -i equal to 392, then 376, and up to so on, 375, such as n -equal to 10 observations are given.
00:16
So here, your strength is normal distribution, that is random variable x follows, normal distribution with mean mu and standard division sigma.
00:24
So we have to find out the value of mu and sigma.
00:27
So here, first by using maximum likelihood estimate, the estimate of mu equal to x bar.
00:36
So here we calculate the value of x bar equal to summation of xi divided by n, a standard division, sigma equal to square root of sigma square, where sigma square equal to 1 upon n minus 1, summation of x i minus x bar bracket square hence we get the sample mean x bar equal to 3844 divided by 10 equal to 384 .4 and sample standard division sigma equal to 19 .8785 so here the estimate of mu height equal to x bar equal to 384 .4.
01:20
Now next we are to find out 95th percentile, 95th percentile.
01:28
So here the formula for percentile becomes percentile equal to x equal to mu plus sigma into z and the value of z at 95 percent equal to 1 .96...