z scores / probability / stats

Question

assume that the scores are normally distributed with a mean of zero and a standard deviation of one.

A) if p(z<a) = .9599, find a.

B) if P(z>b) = .9772, find b.

C) if P(z>c) = .0668, find c

Answer 1

These numbers provided indicate the answers can be obtained from a standard z-table.

To read a typical z-table, the probabilities provided in the main portion of the table represent

P(Z < z) = 0.####

where 0.#### represents the value in the table, and z can be found be connecting the corresponding row-column combination.

Also remember due to an axiom of probability, P(X < x) = 1 - P(X > x). This is useful for B).

Therefore,

A) a = 2.00

B) P(B > b) = .9722 ==> P(B < b) = 1 - .9722 ==> b = -2.00

C) P(C > c) = .0668 ==> P(C < c) = 1 - .0668 ==> c = 1.50