Question

Given a population in which the probability of success is p = 0.60, if a sample of 600 items is taken,

calculate the probability the proportion of successes in the sample will be between 0.58 and 0.64

calculate the probability the proportion of successes in the sample will be between 0.58 and 0.64 if the sample size is 200.

Answer 1

9a)

p = Population proportion = 0.6

q = 1 - = = 0.4

n = sample size = 600

SE =

To find P(0.58 < < 0.64):

Case 1: For between 0.58 to mid vale:

Z = (0.58 - 0.60)/0.02 = - 1

Table of Area Under Standard Normal Curve gives area = 0.3413

Case 2: For from mid value to 0.64:
Z = (0.64 - 0.60)/0.02 = 2

Table gives area = 0.4772

So,

P(0.58 < < 0.64) = 0.3413 + 0.4772 = 0.8185

(b)

n = 200

SE =

Case 1: For from 0.58 to mid value:
Z = (0.58 - 0.6)/0.0346 = - 0.5780

Table gives area = 0.2190

Case 2: For from mid value to 0.64:
Z = (0.64 - 0.6)/0.0346 = 1.1561

Table gives area = 0.3770

So,

P(0.58 < < 0.64) = 0.2190 + 0.3770 = 0.5960