A random sample of size n 100 is taken from a population of

A random sample of size n = 100 is taken from a population of size N = 3,000 with a population proportion of p = 0.34.

Is it necessary to apply the finite population correction factor?

Calculate the expected value and the standard error of the sample proportion. (Round intermediate calculations to 4 decimal places, \"expected value\" to 2 decimal places and \"standard deviation\" to 4 decimal places.)

What is the probability that the sample proportion is greater than 0.37? (Round intermediate calculations to 4 decimal places, \"expected value\" to 2 decimal places and \"standard deviation\" to 4 decimal places.)

Solution

a-1.)
No, as the proportion rate is greater than >0.05
b)
Proportion ( P ) =0.34
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.34*0.66/100)=0.0474

standard error = s.d / Sqrt(n) = 0.0474 /Sqrt(100) = 0.00474
c)
P(X > 0.37) = (0.37-0.34)/0.0474
= 0.03/0.0474 = 0.6329
= P ( Z >0.633) From Standard Normal Table
= 0.2634