Question

In a normal distribution, what is the probability that a data value will fall below the 

data value associated with a z -score of 3.37?
A 99.96%
B 0.04%
C 1%
D 99.95%

Answer 1

A 99.96%

Explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is positive if the raw score is above the mean while the z score is negative if the raw score is below the mean. The z score is given by:

`z=(x-\mu)/(\sigma) \\\\where\ z=z-score,\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation\\\\For\ a\ sample\ size(n):\\\\z=(x-\mu)/(\sigma/√(n) )`

The probability can be gotten from the normal distribution table. Therefore from the normal table:

P(z < 3.37) = 0.9996 = 99.96%