00:01
Now here you look at a survey, right? the survey says that about 16 .2361 % of the adults said they have had someone taking, take over their email cards without the combination, right? so let me denote by p, this value, okay, 16 .2361%.
00:20
And now you run and take a sample of 250 m equals 250 u .s.
00:27
Adults and ask them whether they have had someone take over the email columns without their permission, right? let the number x be, sorry, let x be the number of the adults among these 250 adults, right, who had their email accounts taken over by somebody without permission.
00:53
And this should follow a binomial distribution, right, with p and n, right? you can approximate this binomical distribution by a normal approximation because this sample size is big enough and p is small enough, right? and actually you'll find this to be, of course, the normal distribution will have a mean, which is actually given by n times p and the standard deviation, which is given by n times p and times 1 minus p, okay? and then you can calculate this to be 40 .6, while the standard derivation, which is given by n times p and times 1 minus p, okay? and then you can calculate this.
01:30
And then you can calculate this to be 40.
01:30
Is i found this with 5 .8.
01:35
Now, you can answer a few questions, right? basically, you ask you to find the probability that x is less than 45 or at the most 40 or exact 48, right? so we can find the probability obviously.
01:49
So first we look at a px less than 45, right? now, 45 relies to the rise of the means, right? so if you look at the distribution of x approximately, is a normal distribution, something like this, right? and obviously, this is actually 40 .6.
02:08
That's me, and you look at 45 ways somewhere here, right? and less than 45, so the percentage of probability actually is given by the area under this curve to the left of 45, right? and that area can be given by 1 minus alpha, all over the area of the pair to the right of 45, right? you can find that the alpha from the d score, so the alpha is given by 45 minus 40 .6 over standard division.
02:32
Which is 5 .8, and you'll find this to be given by 0 .76.
02:40
And you look up the z table, you find out of course 22 .3%, or 22 .4%.
02:53
And therefore, you found this to be about 1 minus, you say, about 78 % or 77 .6%.
03:01
So that's a percentage.
03:03
And how about at most 40, right? so you look at another value, which is 40, right? look at 40, which is here, and the most 40...