00:01
Given that probability of success is 0 .9, which is 90 % and sample size is ap.
00:09
First of all, we have to find new value which is expectation of x equal to np, that is 80 into 0 .9 is 72.
00:21
Second one, we have to find standard deviation which is root over npq, that is root over ap into 0 .9 into 0 .1.
00:32
Equal to root over 7 .2 is 2 .683.
00:39
Standard error is sigma by root n, that is 2 .683 divided by root 80, equal to 0 .3.
00:53
Now we have to find probability that p greater than 0 .91, which means the x value is 0 .91 into 0 .91, which means the x value is 0 .91 into 2 .91, 80 equal to 73 .71.
01:10
So probability of x greater than 73 .71 can be solved using normal probability that is 1 minus x less than 73 .71 equal to 1 minus probability of x minus mu by sigma less than 73 .71 minus sigma is where mu is 72 divided by standard error here.
01:35
We have sample size so standard error is 0 .3 1 minus probability of z less than 1 .71 divided by 0 .3 equal to 1 minus probability of z less than 5 .7 this value can be obtained using excel formula are you can see that under the standard normal distribution 99 .7 % of the all values lies between minus minus 3 and plus 3.
02:09
So the area less than 5 is almost 1.
02:16
So 1 minus 1 is 0.
02:18
The probability of x greater than 73 .71 is let x be height of men.
02:33
Given that x follows normal distribution with me new equal to 69 and standard deviation sigma equal to 3.
02:40
And given that sample size, n equal to 5 so x follows normal distribution with mean mu equal to 69 and standard deviation sigma equal to sigma by root n that is 3 divided by root 50 equal 0 .4 to 4 3 .3 so mu of x bars is 69 x standard deviation is 0 .40 4243.
03:14
Now we have to find probability of x bar less than 68 which is probability of x bar minus new divided by sigma less than are equal to 68 minus 6 .s sigma x bar is 0 .4243 equal to probability of z less than minus 1 divided by 0 .43 4 to 4 to 4 3 is probability of z less than minus 2 .357.
03:41
This value can be obtained using the excel formula...