If the mean is 100 and the standard deviation is 15 then what Zscore corresponds to 112

Question

mean = 100

standard deviation = 15

z-score for 112 = x

x = ??

Answer 1

Z=(112-100)/15=12/15=⅘=0.8 which means that 112 is 0.8 standard deviations from the mean.

Using the normal distribution table this Z-score can be translated into a probability.

In this case Z=0.8 corresponds to about 0.788, or 78.8%, which means that about 78.8% of the data are 112 or less. Put another way, there's a 21.2% probability that a data value will be higher than 112, or a 78.8% probability that it will be lower than 112.