00:01
Given annual rainfall follows normal distribution with mean mu equal to 40 and standard deviation sigma equal to 4.
00:16
Now we have to find probability of rainfall is greater than 50 is first standardize the values, that is, z greater than 50 minus mu 40 divided by standardizing.
00:33
Sigma is 4 equal to probability of z greater than 10 divided by 4 is probability of z greater than 2 .5 which can be written as 1 minus probability of z less than 2 .5 the value probability of z less than 2 .5 obtained using excel formula norm .s .d the first parameter is 2 .5 and the second parameter is true that is we want so the probability is 0 .9938.
01:12
Probability of x greater than 50 is 0 .0062.
01:22
Given n equal to 10 years.
01:26
Now we have to find probability of main rainfall is greater than 50.
01:34
It is equal to we know that if sample x follows normal distribution with mean mu and sigma standard deviation, then x bar follows normal distribution with mean mu x bar equal to mu and sigma x bar equal to sigma by root n.
01:56
So probability of x bar minus mu by sigma by root n greater than 50 minus mu is 40 divided by 4 by root 10 equal to probability of z greater than 10 by 1 .2649 is probability of z greater than 7 .9057, which can be written as 1 minus probability of z less than 7 .957...