00:03
Hello friends welcome we have a question here and in this question we have value of me it is given as mean of 85 and a standard deviation is given us of 4 10 so let's solve this question here into the solution part part it is given that given that me that will be will is equal to 85 and standard deviation, deviation, sigma is equal to 10.
00:52
So let's solve our first part a, here by using the normal standard distribution, by using normal standard deviation.
01:12
We can find the z -spoor, z for middle, 98 % as p is lie between minus z greater than or equal to set capital z this is the capital set it will this is smaller and less than or equal to small z positive small z and that is percentage is 68 so when we calculate this will be equal to 0.
01:51
And now we can separateize this as z greater than or equal to small z minus p z greater than or equal to minus small z will be equal to the same value 60.
02:10
0 .60 now when we solve this this will be 2p capital z greater than or equal to small z will be minus 1 is equal to 0 .60 .8.
02:27
So now here 2p capital z greater than or equal to small z is equal to 1 plus 0 .68 that will become 1 .68.
02:45
Now the value for p z greater than or equal to small z is equal to 1 .68 divided by 2 so this will be equal to 0 .8 4 and here we can write now p capital z value of small z is 0 .99 therefore this is equal to 0 .84 so here you can see z is equal to 0 .99 on comparing and z will be equal to minus 0 .99.
03:28
So now we have to use z score formula by using z score formula and that is x is equal to z, niterg by standard deviation added by me, which is green.
03:53
So let's put down the values.
03:55
Z is minus 0 .0 .0 .09 multiplied by 10 and then added by 85 which is the moon.
04:09
So now this will be equal to 75 .1...