A random sample is to be selected from a population that has

A random sample is to be selected from a population that has a proportion of successes p = 0.64. Determine the mean and standard deviation of the sampling distribution of pfor each of the following sample sizes. (Round your standard deviations to four decimal places.)

(a)    n = 30

(b)    n = 40

(c)    n = 50

(d)    n = 70

(e)    n = 120

(f)    n = 220

Solution

a)
Mean ( np ) =19.2
Standard Deviation ( npq )= 30*0.64*0.36 = 2.6291

b)

Mean ( np ) =25.6
Standard Deviation ( npq )= 40*0.64*0.36 = 3.0358
              

c)

Mean ( np ) =32
Standard Deviation ( npq )= 50*0.64*0.36 = 3.3941
              

d)

Mean ( np ) =44.8
Standard Deviation ( npq )= 70*0.64*0.36 = 4.016