Chapter 3, Problem 3.50RE

(a)

To determine

To find: the value z from a standard normal distribution that satisfies each of the following conditions and sketch a standard normal curve with value of z marked on the axis

Explanation of Solution

Given:

The point z with 70% of the observations falling below it

Calculation:

70% = 0.70

Looking in the table for the percent 70% or 0.70 closet value

  $z=0.52$

Graph:

The point z =0.52 with 70% of the observations falling below it which is looking forth.

(b)

To determine

To find: the value z from a standard normal distribution that satisfies each of the following conditions and sketch a standard normal curve with value of z marked on the axis

Explanation of Solution

Given:

The point z such that 90% of all observations are greater than z

Calculation:

Looking in the table for the percent 100%- 90% =10% or 0.10 closet value

  $z=-2.30$

Graph:

The point z =-2.30 such that 90% of all observations are greater than z=-2.30 which is looking forth.

(c)

To determine

To find: the value z from a standard normal distribution that satisfies each of the following conditions and sketch a standard normal curve with value of z marked on the axis

Explanation of Solution

Given:

The 46^th percentile of the standard normal distribution

Calculation:

Looking in the table for the percent 46% or 0.46 closet value

  $z=-0.10$

Graph:

The point z =0.10 with 46% of the observations falling below it which is looking forth.