Question

Computer lecture on going from area to score with normal distribution - Saved to this PC t References Mailings Review View Help Tell me what you want to do In our last computer assignment we leamed how to find the standard normal distribution up to the given score value a, that is we found P[Z <a). We used Excel instead of the standard nornal distribution table and evaluated P(Z<-1.72) with the command NORMDIST(1.T2B1,B2,TRUE) and we obtained 0.042716 approximately. Here Z is standard normal distribution In this exercise we will leam how to go backwards, that is from the probability P(Z < a) to the score a In cell A1 type mean and in cell B1 type 0. That way we are letting mean be zero. Next click on cell A2 and type SD and in cell B2 type 1. That means that we let standard deviation be one. That is, our normal distribution is standard Suppose we know that the percentile of the score is 4 2716% corresponding score. We would like to find the Type 0.042716 in B6. That is the given probability of Zsa. We would like to find the score a. In cell B7 type NORM INV(0.042716,B1,B2). That gives you the score a. We went backwards to-1.72. There is a way to find this score a using the standard normal distribution table, but our result will not be as precise as the one obtained with Excel today Now we do this process for any normal distribution. That is, not only that we do not need the table, but we also do not have to apply the formula to go from standard normal distribution to the given normal distribution. We illustrate that on an example. Suppose at cholesterol has normal distribution with mean 189 and standard deviation 28. Suppose your cholesterol percentile is 60% That is your cholesterol is higher than approximatel 60% of all people in the world we would like to evaluate your cholesterol level using Excel. To do this we first click on cell D1and type 189. That means that we let mean be 189 Next click on cell D2 and type 28. That means that we let standard deviation be 28. This means holestero mabton ts not standard Next, dlick on cell A6 and type Finally click on cell D7 and type -NORM INVID5.D102) Did you obtain approximately Exercie 1 Uine Eacel evaiuate the sote that corresonds to 6 percentie in ztandard probability. Then click on cell A7 and type score Now click on cell D6 and type 6 196 as your cholesterol? Exercises distribution Put your resultin cel Al1 Exercise 2 LetX be normally distributed with mean 89 and standard deviation is Given Preah-36% evaluate a using Excel. Put your result in cell A1s

Answer 1

Exercise 1

We have to find the score that corresponds to 65 percentile in standard normal distribution.

That is, we have to find the score a such that P(Z < a) = 0.65.

The standard normal variable Z has mean 0 and standard deviation 1.

Now in cell A11 of excel we put =NORM.INV(0.65,0,1) so we get 0.3853.

Hence the score that corresponds to 65 percentile in standard normal distribution is 0.3853.

Exercise 2

Let X be normally distributed with mean 89 and standard deviation 15.

Given P(X < a) = 36%

We have to find the score a such that P(X < a) = 0.36

Now in cell A15 of excel we put =NORM.INV(0.36,89,15) so we get 83.6231

Hence, a = 83.6231