00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
Now let me bring up your question here.
00:06
In this question we discuss about the binomial it will be approximated by the normal distribution.
00:15
Let me remind you that if we have the x, it will follow by the binomial nb.
00:23
And then if we have the nb or n times 1 minus 1.
00:30
B, both of them they are greater than 10, and then we can approximate the x by the normal, when the mean of the x is equal to the n times b, standard division the x equal to the square root of n times b times 1 minus b.
00:50
Now in this question here, we are given that the p equal to 0175, and then we have the n equal to 150.
01:02
It will try to test the condition here.
01:04
We see that the n 150 times 0 .75 will be greater than 10 and also 150 times 0 .255 also greater than 10.
01:14
Therefore we setify the condition here and we see that x is followed by the binomial with the n equal to 10 and 150 and then the p equal to 0 .75.
01:32
But we can also approximate the x by the normal, where the mill of x equal to n times b.
01:42
So we get the 150 times 0 .75, then we get equal to 150 times 0 .75, can equal to the 150 times 0 .75, can equal to the 112 .5.
02:07
Also, we will have the standard division on the x.
02:12
It will equal to the square root of the 120 times 0 .75.
02:19
1 minus 0 .75 will be 0 .25.
02:23
And if we do it, times 0 .25, taking the square root can equal to the 5 .3.
02:32
And now we will be able to answer the part i am the question.
02:36
The question asks can let you find the probability that x smaller than 150.
02:42
Now we can appropriate this probability by the z smaller than the 150 minus the mean will be 112 .5 divided by the standard deviation.
03:02
So if we compute it, we get the z will be smaller than 105 minus 5.
03:09
1 1 2 .5 divided by the 5 .3 and equal to the minus 1 .4 2 and to compute this probability i will bring up the z table and i will show you had to use the z table here.
03:29
Let me put the table on the top here for you and here look at the table once you have the z smaller than minus 1 .4 2 minus 1 .4 will be here 2 .2 will be here so so the probability will be equal to 0 .0778.
03:48
And this will be the answer for the a.
03:51
Now for the b, when you find the probability of the x between the 111 and the 121.
04:00
Now for the binomial approximation to the normal, we need to you do the correction here.
04:07
It means that we need to subject the half.
04:13
From the left and plus a half to the right...