4. Of the z-scores: -2.3, +1.0, +0.9, and -0.6 a. Which...

4. Of the z-scores: -2.3, +1.0, +0.9, and -0.6 a. Which z-score corresponds to the smallest raw score? b. Which z-score reflects the raw score having the highest frequency? 5. What proportion of the area under the standard normal curve would you expect to be... (Remember to draw the picture of the normal distribution and shade the region designated in the question. Then use the z-score tables in the book) a. between z = -1.2 and z = + 0.6? b. below z = 1.4? c. below z = -2.6? d. above z = -2.0?

Transcript

00:01 Hello friends, let us talk about this problem in which we have been given that out of the z scores, okay, so particularly we have been given some z scores and we have to firstly answer the first part in which it is said that which z score correspond to the smallest raw score.

00:17 So let us see the solution.

00:19 First of all, i can say that let let raw score equals x.

00:26 Okay, so it is equal to x.

00:28 Now i can also say from here that jad value is equal to jad value equals to x minus mu over standard deviation right so standard deviation can also be written as sigma i am writing it over here as such now from here if you modify the equation you will have x equals j that is standard z a standard deviation plus mu that is we have been writing the equation as z sigma plus mu okay so this is the equation what we have obtained after modifying the z value equation so let me just put it in a box now let us move ahead and try to solve the first part of the solution so this was actually the introduction kind of thing now the first part of the solutions will be minus point let me write it it will be minus point six would compare to the smallest would correspond to the smallest roy score okay so minus point six would correspond would correspond i can write that would correspond to the smallest smallest roy score smallest roy score i hope that you have got this problem well that you have understood this solution back now let us talk about the be part of the solution which i have to answer that in for which the answer will be the values which are closest to middle have the highest frequency so i can write the values the values which are which are closest clo s e s d closest to middle m m e wd l -e -d middle have the values have the highest frequency have the highest h -i -g -h -e -h -e -t highest frequency that is it will give us the value for minus 0 .6 okay so this is the answer for this problem and i can say that first part of the second problem can be solved by using this formula that between between z equals minus 1 .2 and z equals 0 .6 can be solved by drawing a graph we will be required to draw a graph over here to understand this problem matter and i will try to highlight the graph so that you understand the graph in a more decisive manner so it will be like this and then if i draw a graph in such a way that it just cut out at this point in the middle then it will look like this somewhat okay so don't go to the exact exact graphical values because it may not be so accurate because i have drawn it on with my hands only i haven't used any software so it will be zero and here it will be 0 .6 here it is point minus 1 .2 so now i can say that t1 that is let me write it it will be t1 so it becomes 0 .6 equals 0 .7257.

04:11 Now, here i can say that t minus 1 .2 equals 0 .1151.

04:22 Okay, so let me just put this point somewhat down and let me just erase it.

04:27 It will be like this.

04:28 Now, if i assume this is my first value and this is my second value.

04:34 So, i can say that the area between this shaded portion, that is this particular area, which i am just shading right now, will have the value.

04:45 Let me just show you this whole area.

04:48 Okay...

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