standard normal curve

Question

Suppose baby kittens' weights are normally distributed with a mean of 13.1 and a standard deviation of 1.5. 

The Z-score tells you how many units above the average (if Z-score is positive) or below the average (if Z-score is negative) any particular baby kitten's weight is. 

Find the baby kitten weight that corresponds to the following Z-scores. 

1. Use the formula Z=X−μσZ=X-μσ where μμ is the mean, σσ is the standard deviation, and XX is the baby kitten weight. 
2. Z=−1.13, X=?
3. Z=−0.23, X=?

Answer 1

z = (x - mean) / sigma

x = sigma * z + mean

for mean = 13.1 and sigma = 1.5

x = 1.5 * z + 13.1

for z = -1.13, x = 1.5 * -1.13 + 13.1 = 11.405

for z = -0.23, x = 1.5 * -0.23 + 13.1 = 12.755