Question

According to the National Center for Health Statistics (2009), the average height for an adult female in the United States is 63.8 inches (5 foot 3.8 inches) tall. Although the public statistics do not state a standard deviation, let's estimate the standard deviation as 2 inches. Use this information to answer the following questions. 5 pts D Question 13 What proportion of women in the United States is taller than 65 inches? DQuestion 14 5 pts What proportion of women in the United States are between 62 inches and 64 inches? D Question 15 5 pts The proportion of women below a z score of -2.1 is

Answer 1

Question 13:

$\mu$ = 63.8

$\sigma$ = 2

To find P(X>65):
Z = (65 - 63.8)/2 = 0.6

Table of Area Under Standard Normal Curve gives area = 0.2257

So,

P(X>65) = 0.5 - 0.2257 = 0.2743

Question 14:

To find P(62 < X< 64):
Case 1:
For X from 62 tomid value:

Z = (62 - 63.8)/2 = - 0.9

Table gives area = 0.3159

Case 2: X from mid value to 64:
Z = (64-63.8)/2

= 0.1

Table gives area = 0.0398

So,

P(62 < X< 64) = 0.3159 + 0.0398 = 0.3557