Question

(1 point) Use the value of from Table A that comes closest to satisfying the condition.
(a) Find the number zz such that the proportion of observations that are less than zz in a standard Normal distribution is 0.3174.
(b) Find the number zz such that 93.88% of all observations from a standard Normal distribution are greater than zz.

(a)  
(b)  

Answer 1

(a)

Proportion of observations that are less than Z in a Standard Normal Distribution = 0.3174

This is equivalent to area from mid value to Z on LHS = 0.5 - 0.3174 = 0.1826

Table of Area Under Standard Normal Distribution gives Z = - 0.475

So,

Answer is:

- 0.475

(b)

The number Z such that 93.88% of all observations from a standard Normal distribution are greater than z is equivalent to area = 0.9388 - 0.5 = 0.4388 from mid value to Z on LHS.

Table of Area Under Standard Normal Distribution gives Z = - 1.545

So,

Answer is:

- 1.545