Part II. Make sure you show all the necessary work to get full credit. 11. (17 p
ID: 3365449 • Letter: P
Question
Part II. Make sure you show all the necessary work to get full credit. 11. (17 pts) The Harvard College Alcohol Study finds that 67% ofall college students support efforts to "crack down the underage drinking". The administration of UNCW surveys an SRS of 100 students and finds that 69 support a crackdown on underage drinking. All answers Round to 3 decimal places in each step. a) What is the mean of the sample proportion p? Give both mathematical notation and numerical solution. b) What is the standard deviation (SD) of the sample proportion p? Give both mathematical notation and numerical solution. c) What is the sampling distribution of the sample proportion p of a SRS of 100 students at UNCW? d) For UNCW's SRS, what is the sample proportion p of these 100 students who support a crackdown on underage drinking at UNCW? e) What is the probability that the proportion in an SRS of 100 students is as large as or larger than the result of the administration's sample at UNCW? CYou need to specify how to get Z-score, draw Standard Normal curve, and indicate which part you're looking for to get full credits. A solution with only a number will receive only the credi for last step.)Explanation / Answer
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
a.
proportion ( p ) = 0.69
b.
standard Deviation ( sd )= sqrt(PQ/n) = sqrt(0.69*0.31/100)
=0.046
c.
sample distribution follows normal and X ~ N ( 0.69, 0.046^2)
d.
the number os tudents who support in a sample distribution 100 students
who support a crackdown on underage = 69/100 = 0.69
e.
GREATER THAN
P(X > 0.67) = (0.67-0.69)/0.046
= -0.02/0.046 = -0.435
= P ( Z >-0.435) From Standard Normal Table
= 0.668