00:01
Hi, i'm david and i'm here to help the answer your question.
00:03
Now let me bring up your question here.
00:06
In the question here, we'll discuss about the normal distribution.
00:09
Let me remind you that if the x that followed by the normal, with the mean and standard deviation, and if we turn the x, we minus the mean of a standard deviation, we obtain the standard normal.
00:20
Sorry, obtain the z here.
00:23
Now the question tells us that we have the normal x with the mean equal to 9 .8 and the standard deviation.
00:30
Equals 1 you didn't correct for the a.
00:33
Now for the b, want to find the probability then the x it will be between the 10 .3 and the 11 .6.
00:43
Now to find this probability we need to use the formula here to rewind the x into the z and to do it we need to take the 10 .3 minus the mean will be the 9 .8 divided by the standard division 1.
01:00
We do the same thing on the right then we get equal to the probability of the z it will be between the 10 .3 minus the 9 .8 equal to the 0 .5 11 .6 minus 9 .8 equal to the 1 .8 to find this probability i need to bring up the z table so let me copy the z table here and let me put the table on the right here.
01:33
Notice the table i bring here and has negative g score with the probability on the left tail.
01:38
So we need to convert this probability to make it compatible.
01:42
Now this will be the area on the right.
01:45
So because of the symmetry, i can turn it into the left.
01:48
So this it could be between minus 1 .8 to the minus 0 .5.
01:53
Then i will take the bigger one, i will minus the smaller one.
02:01
And now i can use the table.
02:03
When the g score equal to minus 0 .05, the corresponding probability will be 0 .3 .85.
02:10
And the minus 1 .8, we have the corresponding probability 0 .0 .0 .059...