Arandom sample is to be selected from a population that has a proportion of successes p = 0.61. determine the mean and standard deviation of the sampling distribution of p? for each of the following sample sizes. (round your standard deviations to four decimal places.)

(a) n = 20

mean
standard deviation

(b) n = 30

mean
standard deviation

(c) n = 40

mean
standard deviation

(d) n = 60

mean
standard deviation

(e) n = 110

mean
standard deviation

(f) n = 210

mean
standard deviation

We know that the mean and standard deviation of the sampling distribution of p is given by :-

, here p is the proportion of successes ion and n is the sample size.

We are given that ,

Proportion of successes p = 0.61

a) n= 20

The mean and standard deviation of the sampling distribution of p is given by :-

So,  mean  = 0.61

standard deviation = 0.1091

(b) n = 30

mean

=0.61

standard deviation  =0.0891

(c) n = 40

mean

=0.61

standard deviation  =0.0771

(d) n = 60

mean  =0.61

standard deviation  =0.0630

(e) n = 110

mean  =0.61

standard deviation  = 0.0465

(f) n = 210

mean  =0.61

standard deviation =0.0337

step-by-step explanation:

a'(12.5,11.25)

slope=(y1-y2)/(x1-x2)