A random sample of size n = 93 is taken from a population of size N = 674 with a

Question

A random sample of size n = 93 is taken from a population of size N = 674 with a population proportion of p = 0.68.

A.

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.)

B.

What is the probability that the sample proportion is less than 0.54? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

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.)

B.

What is the probability that the sample proportion is less than 0.54? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Explanation / Answer

a.
expected value = Proportion ( P ) =0.68
standard error of the sample ( se )= Sqrt (P*Q /n) = Sqrt(0.68*0.32/93)=0.0484
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

b.
P(X < 0.54) = (0.54-0.68)/0.0484
= -0.14/0.0484= -2.8926
= P ( Z <-2.8926) From Standard Normal Table
= 0.0019                  

0.19%

sample proportion is less than 0.54

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