00:01
Hello everyone.
00:03
So in this question it is given that mu is equal to 187, sigma equals to 288 and x equals to 210.
00:22
We need to compute probability of x greater than equals to 210 given that x is following normal distribution with mean mu and variance sigma square.
00:41
So probability of x greater than equals to 210 is same as converting x into standard normal variant, that is z is equals to x minus mu divided by sigma.
00:53
So probability of z greater than equals to 210 minus 187 divided by 28, that is probability of z greater than equals to 0 .82, which is as 1 minus probability of z less than 0 .8 to.
01:33
From standard normal table we see that this value is equals to 0 .739.
01:40
So this becomes 0 .2061 or 20 .61 percentage.
01:53
Coming to the part named as c, so here given permissions of mu which is 187, sigma which is 286, x1 that is 150 x2 that is 160 we need to compute the probability that x lies between x1 and x2 that is 150 and 160 so again we'll converting x into standard normal variant which becomes probability 150 minus 187 divided by 28 less than equals to z less than equals to 160 minus 187 divided by 28.
02:52
That is equal to probability that z lies between minus 1 .32 to minus 0 .96.
03:08
Or this is same as probability that z is less than equals to 0 .96 minus probability that z is less than equals to minus 1 .32...