Answer to Question #136196 in Statistics and Probability for Dicksen Munjimi

Question

Question 1 [10]
In the years 2007 a total 3500 UNAM students out of a sample 6000 who applied for NSFAF
student loans were successful.
Required:
a. Point estimate of p.
b. Point estimate of the proportion standard deviation (3)
c. What is the probability that the proportion of students who passed the course
is more than 0.55 (5)

Answer 1

p=r/n=3500/6000=0.58

sd=$\sqrt{(pq)/n}=\sqrt{(0.58*(1-0.58))/6000}=0.00637$

P(p'>0.55)=1-P(p'<0.55)

P(p'<0.55)

z=(x-p)/sd=-0.03/0.00637=-4.7, using table P(p'<0.55) =0.000001

P(p'>0.55)=1-0.000001=0.999999