Question 433383
In a local university, 40% of the students live in dormitories. A random sample of n = 80 students is selected for a particular study. 
(a) What is the sampling distribution of P?
---
Note: You have not provided a description of P.
Is it the proportions of all samples of size 80?
Is it the 
----
If it is the population:
mean = np = 80*0.4 = 32
std = sqrt(npq) = sqrt(32*0.6) = 4.3817..
---------------------------------------------
If it is the proportions of samples of size 80:
mean =  0.4
std = sqrt[0.4*0.6/80] = 0.0548
-------------------------------------
 Please provide its general shape, its standard deviation, and its mean.
---- 
(b) What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50?
z(0.3) = (0.3-0.4)/0.0549 = -1.8215
z(0.5) = (0.5-0.4)/0.0549 = 1.8215
---------------
P(0.3< x <0.5) = (-1.8215< x < 1.8215) = 0.9315
===============
Cheers,
Stan H.