Question

Suppose a simple random sample of size n equals 50 is obtained from a population whose size is Upper N equals 20 comma 000 and whose population proportion with a specified characteristic is p equals 0.6 . Complete parts ​(a) through​ (c) below. ​(b) What is the probability of obtaining x equals 32 or more individuals with the​ characteristic? That​ is, what is ​P(Modifying Above p with caretgreater than or equals 0.64​)? ​P(ModifyingAbove p with caretgreater than or equals 0.64​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

(b)

To find P():

N = Population Size = 20,000

n = Sample Size = 50

Applying Finite Population Correction (FPC) Factor, we get:

Test Statistic is given by:
Z = (0.64 - 0.60)/0.0678

= 0.59

By Technology, Cumulative Area Under Standard Normal Curve = 0.7224

So,

the probability of obtaining x equals 32 or more individuals with the​ characteristic is given by:

P():= 1 - 0.7224 = 0.2776

So,

Answer is:

0.2776