Question

The proportion of BYU-Idaho students that are married is p = .25. You plan to take a random sample of 100 students and calculate the proportion of married students in your sample. Find the mean, standard deviation, and shape of the distribution of the sample proportions calculated from samples of size 100. Use this information for all the parts.

Answer 1

`p \sim N (p, \sqrt{(p(1-p))/(n)})`

And the parameters are given by:

The mean is given by:

`\mu_p = 0.25`

The standard deviation is:

`\sigma_(p) =\sqrt{(0.25(1-0.25))/(100)}= 0.0433`

And the distribution would be bell shaped and normal

Explanation:

For this case we have the following info given :

p =0.25 represent the proportion of BYU-Idaho students that are married

n = 100 represent the sample size

And for this case we can check the conditions in order to use the normal distribution:

1) np = 100*0.25 = 25>10

2) n(1-p) =100*(1-0.25)= 75>10[/tex]

3) Independence is assumed in each sample and the probability is the same

So then we have all the conditions satisfied, and the distribution for the proportion would be given by:

`p \sim N (p, \sqrt{(p(1-p))/(n)})`

And the parameters are given by:

The mean is given by:

`\mu_p = 0.25`

The standard deviation is:

`\sigma_(p) =\sqrt{(0.25(1-0.25))/(100)}= 0.0433`

And the distribution would be bell shaped and normal