All right. So, students weights have a mean value of 62.5 kg. With a standard deviation of 2.7 kg. Alright. Is a normal distribution. So, we're gonna be using the normal distribution formula A minus mu over omega. Where a is going to be the weight in kilograms. All right. And this formula always assumes that we're talking the percentage of uh uh of weight that is less than than whatever you're looking for than a. It's always less than that's the key. Yeah. So, for part A I want to know How many of the 1000 total students. Yeah. Mhm. What% 55 kg? Okay, So, it just gets plugged into the formula 55 minus 62.5 Over 2.7. So that's seven point 5/2 7.0.5 inside the parentheses. So, this part inside the princess gives you a value of three and that's the Z value. We have a Z equal to three. So, if you look at your your Z. Table in the back of your book, A value of three Has a percentage of 99.87%. Okay, Excuse me. This is negative three negative three has. Yeah. A wait. 0013 or .13%. Okay, so .13% of the 1000 students. So if you multiply that by 1000, that is about 1.3 students. Mhm. You'd expect to weigh less than 55 kg. Okay. For part B we want to know. Mhm. Between 60 and 65 kg. Alright, Whenever you have a range always start with the largest and take away the smallest. Mhm. So Again, for Formula 65 -62.5 over 2.7 minus Normal distribution of 60 -62.5 -2.7. So this is 2.5 divided by 2.7 which is a z value of .93 and the second one is the z value of negative 10.93 Mhm. And then on your Your chart, .93 is 82.38%. And negative .93 is 17.62%. Mm. So, if you subtract those, 82.3, -17.62, That is 64. Mhm .76%. So 64.76% of students have a weight between 60 and 65 kg. Alright, part. See how many of these students would you expect to have? White equal to 63 kg? Yeah. So since we have a continuous distribution here, meaning that you have a continuous and infinite amount of possible weights these students could have, there's you can't make a statement about equal to some number. So the probability are that the number of students who would expect to equal 63 exactly, We have to say is 0%. If if the students could only way sick like integer values for example, um then we could say something about this, but since They could weigh 63.1, 63.001 and so on. We there's no way you can you can just say equal to some number. So that's 0%. And then finally we want to know How many students would expect to have weights greater than 61 kg. All right, so plug into the formula 61 -62.5 over 2.7. That is negative 1.5 Divided by 2.7. So this is a Z value of- .56. And if you look on your table, .56 is 71.23%. All right now, you got to keep in mind this is a greater than so you get Less than you have to subtract it from one. So the actual percentage of students greater than 61 kg Is 28.77%. And then to get an actual number of students multiply that by 1000 1000 times .2877. Yes, we would expect 287.7 students to have a weight greater than 61. Mm. Mhm. That this this is not the correct number. I looked at positive .56 negative .56 Should instead be 28.77%. But when you subtract it from one, you'll end up with 71.23%. So the final number, when you multiply it by a 1000 lined up, we would expect 712.3 students to have a weight greater than 61 kg.