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CHALLENGE The graphing calculator screen shows the graph of a normal distribution for a
large set of test scores whose mean is 500 and whose standard deviation is $100 .$ If every test
score in the data set were increased by 25 points, describe how the mean, standard deviation, and graph of the data would change.

So we want to find the Z score of 25 if the meanest 25 in the standard deviation is five. So 25 is our value minus 25 which is our mean divided by our standard deviation of five gives us a Z score of zero.

You dis problem with true Cochran Thescore off the same genocide has me 2500 standard duration into five. And then now, this time, actually, see you go to a 125 on starting the equation we can get. The reality is the one 125 reach minus 25 and divide to age. Do actual five years ago to 20 This is

So for this problem, we're looking at the 25th percentile and this is representing, or this is the same thing as a knee area of 0.25 So you can either use thes standard, normal table or technology to solve this problem. I use my graphing calculator. So I used the INS norm function, which gives us a Z score that represents the area we input. So first, well, input that area of 0.25 and then we need the mean and standard deviation of the standard normal curve, which is, uh, centered at zero. And the standard deviation is one. So this gives us answer of negative 0.67 So is the score of negative 0.67 represents the 25th percentile.

Okay, So in this question, there are 65 randomly selected car sales persons. So R N is equal to 65. This is our sample size, and 14 people answered that they sell three cars. So let me just write this in order. So three, three, three, This will go on 14 times, right? This is this is 14 times. Okay, then. 19 self, four cars, then 19 people generally sell four cars. 19 people sell four cars and 12 self five cars. Then after that, 55 this is 12 times. Okay, this is 12 times, okay? And then nine people sell six and 11 sells seven. Over nine people sell six, 66 This will be nine times if I arranged this, and then 11 of them sell seven cars. There will be 11 7th. Okay, this will be 11 times. All right. So this is all the information that we have, and this is all we need. Now, what will be 50th percentile? 50th percentile means the middle point. Right? What is going to be the midpoint? We have arranged this in order, which is the middle value. 65 by two is giving me 30 2.5. But what exactly do we take? We can take either 32 or 33 right? So if I look at this 1st 14 values are trees and then from 15th all the way up to 33rd value, right from 15 all the way to 33. All values Air Force. Right? So what is going to be the middle value middle value, where value meets, remember, we're not taking the midpoint us like the average or something. We're taking the middle value means over here. 13th, Second values, also for and 33rd value is also for so well. The answer in this case is for what is going to be if you arrange all the values in an order, what is going to be the middle value? This is the simple meaning or 58% time right. Which means half the values are less and have the values are more so We can clearly see that there are going to be 19 force. So the middle number is obviously going to be from this lot. And hence we can say that the answer is food