# Assignment: Z-score question

#### jrod72

##### New Member
Assume the distribution is normal in form with a mean of 52 and standard deviation of 3. Find the scores that would correspond to the 35th, 60th and 75th percentiles.
What is the process to find the answer?

#### jrod72

##### New Member
Assume the distribution is normal in form with a mean of 52 and standard deviation of 3. Find the scores that would correspond to the 35th, 60th and 75th percentiles.
What is the process to find the answer?
for the 35th percentile i got 53.17 but when i calculated the 60th percentile i got 52.75

#### SmoothJohn

##### New Member
Take a look at your answers for reasonableness. In a normal distribution

mean=median=mode.

So the median--the 50th percentile--has to be 52.

How did you calculate your current answers?

John

#### jrod72

##### New Member
for the 35th percentile i used the equation
X= Mean + (z)(standard dev)
x = 52 + (0.39)(3)
x = 53.17
i re did it and realized that instead of adding it i subtracted it because it is less than the mean and came up with 50.83. I used the Z of -0.39 because the area below Z is 0.3483

For the 75th percentile i used a z score of 0.67 and came up with 54.01 which makes sense and the 60th percentile a z score of 0.25 and got 52.75