Academic advising: in 2014, the community college survey of student engagement reported that 32% of the students surveyed rarely or never use academic advising services. suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. in a simulation we select random samples from this population. for each sample we calculate the proportion who rarely or never use academic advising services. if we repeatedly obtain random samples of 200 students, what will be the mean and standard deviation of the sampling distribution of sample proportions?

= 0.42

= 0.0349

Step-by-step explanation:

Given:

Probability that students surveyed rarely or never use academic advising services = 32% = 0.32

In reality, students rarely or never use academic advising services at their college = 42% = 0.42

Sample size, n = 200

The sampling distribution of sample proportion will be approximately normal with mean

therefore,

Mean, = p

or

= 0.42

now,

the standard deviation is given using the formula

on substituting the respective values, we get

or

= √0.001218

or

= 0.0349

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )