A random sample size n= 225 is taken from a population with population P=0.55 A.

Question

A random sample size n= 225 is taken from a population with population P=0.55

A. Calculate the expected value and the standard error for the sampling distrituion 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. Wha is the probability that a sample proportion is between 0.50 and 0.60. ( Round intermediate calcuations to 4 decimal places ,"z" value to 2 decimal places, and final answer to 4 decimal places.)

C.What is the probability that the sample proportion is less than 0.50? ( 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 ) =0.55
standard error = Sqrt (P*Q /n) = Sqrt(0.55*0.45/225) = .0332
Normal Distribution = Z= X- u / sd ~ N(0,1)      

b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.5) = (0.5-0.55)/0.0332
= -0.05/0.0332 = -1.506
= P ( Z <-1.506) From Standard Normal Table
= 0.06603
P(X < 0.6) = (0.6-0.55)/0.0332
= 0.05/0.0332 = 1.506
= P ( Z <1.506) From Standard Normal Table
= 0.93397
P(0.5 < X < 0.6) = 0.93397-0.06603 = 0.869              
          
c.
P(X < 0.5) = (0.5-0.55)/0.0332
= -0.05/0.0332= -1.506
= P ( Z <-1.506) From Standard Normal Table
= 0.0655              

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