00:02
Hello students, according to the given question we have to find the probability values.
00:07
So, given the mean mu is equal to 400, sigma is equal to 70, n is equal to 125.
00:16
X follows normal distribution with mean mu and variance sigma square.
00:22
In the a bit to find probability that x bar is within plus or minus 8 of population mean.
00:31
So, that means we can write it as probability of 400 minus 8 less than x bar is less than 400 plus 8.
00:43
So, that is equal to probability of 392 less than x bar is less than 408.
00:50
So, that will be equal to probability of 392 minus 400 divided by 70 divided by square root of 125 is less than x bar minus mu by sigma by square root of n is less than 408 minus 400 divided by 70 divided by square root of 125.
01:17
So, that will be equal to probability of minus 1 .2778 less than z less than 1 .2778.
01:27
From z table the value is 0 .7987...