Question

Section P.5: Density Curves and the Normal Distribution

Example 1: Find the specified areas for a standard normal density, and sketch the area. (a) The area below z = 0.8 (b) The area above z = 1.2 (c) The area between z = -1 and z = 2

Example 2: Find endpoints on a standard normal density with the given property, and sketch the area.

(a) The area to the left of the endpoint is about 0.20.

(b) The area to the right of the endpoint is 0.4.

(c) The area between ± z is 0.80.

Quick Self-Quiz: Standard Normal Distribution Find the specified areas for a standard normal density, and sketch the area.

(a) The area above 2.58

(b) The area below –1.32

(c) The area between 0.85 and 1.35

Find endpoints on a standard normal density with the given property, and sketch the area.

(a) The area to the right of the endpoint is 0.70

(b) The area to the left of the endpoint is 0.10

(c) The area between ±Z is 0.90 ?

Example 3:

Find the specified areas for a normal density. (a) The area above 62 in a N(50,10) density. (b) The area between 5 and 8 in a N(10,2) density.

Example 4:

Find endpoints on the given normal density curve with the given property.

(a) The area to the right on a N(10,4) density curve is about 0.05.

(b) The area to the left on a N(100,25) density curve is about 0.35.

Quick Self-Quiz:

Weights of Newborns Suppose weights of newborn babies in one community are normally distributed with a mean of 7.5 pounds and a standard deviation of 1.2 pounds.

(a) Use the 95% rule to sketch a graph of this normal density curve. Include a scale with at least three values on the horizontal axis.

(b) What percent of newborns weigh less than 5 pounds?

(c) What percent of newborns weight more than 11 pounds?

(d) If a newborn baby is at the 15th percentile for weight, what is the baby's weight?

Answer 1

Example1:

(a) The area below z = 0.8

-3 -2 -1

(b) The area above z = 1.2

2 3 2 2 3

(c) The area between z = -1 and z = 2

3 2 0 2 3

Example 2:

(a) The area to the left of the endpoint is about 0.20.

Z=-.8416

3 2 2

(b) The area to the right of the endpoint is 0.4.

Z=0.2533

3 2 2 3

(c) The area between ± z is 0.80.

between -1.282 and 1.282 or between +/- 1.282

3 2 0 3