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Let X be normal random variable and that E(X) = 1 and sd(X) =What percentile corresponds to X =1.77 What percentile corresponds to X =4 What percentile corresponds...

Question

Let X be normal random variable and that E(X) = 1 and sd(X) =What percentile corresponds to X =1.77 What percentile corresponds to X =4 What percentile corresponds to X =-19. What percentile corresponds to a X = 0,33,

Let X be normal random variable and that E(X) = 1 and sd(X) = What percentile corresponds to X =1.77 What percentile corresponds to X =4 What percentile corresponds to X =-19. What percentile corresponds to a X = 0,33,



Answers

Assume that the random variable $X$ is normally distributed, with mean $\mu=50$ and standard deviation $\sigma=7 .$ Find each indicated percentile for $X .$ The 38th percentile

This is again similar to the last two questions that we did. Now, if this is my standard normal curve, if this is my standard normal curve and I say that this is myself statistic, I want the 81st percentile, right? It means that 81% of value should be behind it. So this should be 0.81 or the value in the tail. That is a P value for this corresponding Z statistics should be 0.19 Okay, now I have my formula. For those that statistic right Z is equal to X minus mu by sigma. Now, you know, uh, I have to find the value of Z for with the p values 0.19 So I use my critical value calculator. I put an alpha 0.19 and I get my Z at 0.8779 So this is 0.8779 is equal to X X is unknown minus mule, which is 50 upon sigma. We're just using the formula for disease statistics, and sigma happens to be seven in this case. Okay, so this is 0.8779 into seven plus 50. So our answer is 56.14 56.1 for this is 81st percentile. Yeah.

Now, This time we want to find the 90th percentile. Right. This is similar to the last question. This is a X, which, as mean as 50 and sigma is seven. Okay, now we want 90th percentile, which means that if this is my standard normal cough in terms of Z value, if this is the set value that I want this is the zebra to this time. Okay? Not this. Okay, we just made Okay, let me just it Is this okay? So if this is the value that I want, I want 19% which means that its P value should be 0.1. With me, the 90% of the values fall behind it. Right. So this has to be 0.9. Okay, So how do I find this Z statistic? I use the critical value calculator I put in my alpha 0.1, and I get Z value as 1.2816 So this is one point 2816 and that's really positive, right? Because I want 90% values through behind it, so it will definitely be more than zero. So this is positive. So my answer How do I reach my answer? The value of X 1.2816 is equal to X minus 50 by seven. Right. This is just the formula for the Z statistic. The only difference is that we know the Z statistic this time and X is unknown. So let us just use a calculator. Seven into 1.2816 plus 50. So our answer is 58.97 This is our 90th percentile 58.97 This is our 90th person time.

Okay, so X is a random variable with mean 50 and standard deviation seven. So this is the mean, which is 50 and sigma is seven. Now, I want to find the ninth person time. So let us look at the standard normal cup. Nine percentile means that if this is my Z value, this area should be equal to 0.9 which means I want to find a Z value which has p value of 0.9 And what I do over here is I use a critical value calculator where I put an alpha 0.9 and I get my Z value to be 1.3408 Right, But since this is on the negative side, we'll put a negative over here. And what do we want? We want to find that particular value of X, beyond which the P value is 0.9 right, for which the P value will be 0.9 Okay, so we put in the value of Z minus 1.3408 is equal to X minus 50 by 7. 50 is the mean seven is the standard deviation, right? We don't want just the value upset Z we found out. Now we want the value of X. So you put in the equation. And the answer that we get is 40.6144 So this is 40.61 for For this is the ninth percent time. This is our answer.


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