Given X~N(5,36)

Question

1. The 50th percentile is?

2. The 10th percentile is?

3. The 90th percentile is?

4. The 20th percentile is?

5. The 75th percentile is?

 

Not sure how to do this. Please help! Thanks!

Answer 1

The notation X~N(5,36) means that X has a Normal distribution with a mean of 5 and a variance of 36.  The standard deviation is the square root of the variance so it is equal to 6.  

 

The relationship between the standard normal variable z and the unstandardized variable x is given by 

 

z = (x - mean) / (standard deviation) = (x - 5) / 6 

 

which implies that (x - 5) = 6*z  so  x = 6*z + 5 

 

So first figure out what z value corresponds to the given percentiles in the standard Normal table and then convert these z values to the corresponding x values.  

 

50th percentile  ==>  P = 0.5  ==>  z = 0  ==>  x = 5

10th percentile  ==>  P = 0.1  ==>  z ~ -1.28  ==>  x = -2.68 

90th percentile  ==>  P = 0.9  ==>  z ~ 1.28  ==>  x = 12.58

20th percentile  ==>  P = 0.2  ==>  z ~ -0.84  ==>  x = -0.04

75th percentile  ==>  P = 0.75  ==>  z ~ 0.67  ==>  x = 9.02  

 

You may get slightly different values for z if you use a program or statistical calculator.  I just picked the closest values from a Z table that goes to 2 decimal places for z.