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 = 0.69. Determine the mean and standard deviation of the sampling distribution of p? for each of the following sample sizes.

(a)    n = 20

(b)    n = 30

(c)    n = 40

(d)    n = 60

(e)    n = 110

(f)    n = 210

Solution

(a)    n = 20

mean=n*p=20*0.69 =13.8

standard deviation= sqrt(n*p*(1-p))

=sqrt(20*0.69*(1-0.69))

=2.068333

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(b)    n = 30

mean=n*p=30*0.69 =20.7

standard deviation= sqrt(n*p*(1-p))

=sqrt(30*0.69*(1-0.69))

=2.53318

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(c)    n = 40

mean=n*p=40*0.69 =27.6

standard deviation= sqrt(n*p*(1-p))

=sqrt(40*0.69*(1-0.69))

=2.925064

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(d)    n = 60

mean=n*p=60*0.69 =41.4

standard deviation= sqrt(n*p*(1-p))

=sqrt(60*0.69*(1-0.69))

=3.582457

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(e)    n = 110

mean=n*p=110*0.69 =75.9

standard deviation= sqrt(n*p*(1-p))

=sqrt(110*0.69*(1-0.69))

=4.85067

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(f)    n = 210

mean=n*p=210*0.69 =144.9

standard deviation= sqrt(n*p*(1-p))

=sqrt(210*0.69*(1-0.69))

=6.702164