Question

1. The birthweight of female lambs is normally distributed with a population mean of 10.6 pounds and standard deviation of 1.3 pounds.

a. What is the probability that the next lamb will have a birthweight greater than 11.2 pounds?

b. What is the probability that a sample of 25 lambs and their birthweight will have a sample mean birthweight greater than 11.2 pounds?

2. In the United States the population has 12.4% left handed people. A sample of 100 people is taken. What is the probability that more than 14 people are left handed?

Answer 1

(1)

(a)

= 10.6

=1.3

To find P(X>11.2):

Z = (11.2 - 10.6)/1.3 = 0.46

Table of Area Under Standard Normal Curve gives area = 0.1772

So,

P(X>11.2) = 0.5 - 0.1772 = 0.3228

So,

Answer is:

0.3228

(b)

= 10.6

=1.3

n = 25

SE = /

= 1.3/ = 0.26

To find P(X>11.2):

Z = (11.2 - 10.6)/0.26 = 2.31

Table of Area Under Standard Normal Curve gives area = 0.4896

So,

P(>11.2) = 0.5 - 0.4896 = 0.0104

So,

Answer is:

0.0104

(2)

n = 100

p = 0.124

q= 1 - p = 0.876

= np = 100 X 0.124 = 12.4

To find P(X>14):

Applying Continuity Correction:

To find P(X>14.5):

Z = (14.5 - 12.4)/3.2958 = 0.64

Table of Area Under Standard Normal Curve gives area = 0.2389

So,

P(X>14) = 0.5 - 0.2389 = 0.2611

So,

Answer is:

0.2611