Posted by Jennifer on .
A set of 50 data values has a mean of 27 and a variance of 16.
I. Find the standard score (z) for a data value = 19.
II. Find the probability of a data value < 19.
III. Find the probability of a data value > 19.
statistics help needed -
The z-score is (19-16)/27 = +1/9 = 0.111
P(z<0.111) = 0.544
P(z>0.111) = 0.456
There are table and online computational aids to give you the P(z) values for a normal distribution. The number 50 is not needed.
There many be a more accurate way to do this using the probabilities of each integer data value, including 19.