Question

10. Suppose the proportion of all college students who have changed their major in the last two semesters is 60%. If a class of 200 students is considered. What is the probability that the proportion of students who may change their major in the next 2 semesters are more than 115?  

Answer 1

Here we have given that

the proportion of all college students who have changed their major in the last two semesters is 60%

P= population proportion=60%=0.60

n= sample size = 200 students

X= No of students who change their major in next 2 semester= 115

= sample proportion ==0.58

Now, we want to find the probability that the proportion of students who may change their major in the next 2 semesters are more than 115

Here,

n*P= 200*0.60 =120 > 10

n*(1-P)= 200*(1-0.60) = 80 >10

Here we can use the normal approximation to the normal

We know that

the mean of all sample proportion is the population proportion.

= P = 0.60

And

=  

=

=0.0346

Now, we want to find the probability that the proportion of students who may change their major in the next 2 semesters are more than 115

i.e

Now for finding this probability first we find the Z-score

= = -0.58

Now,

=1- P(Z< -0.58)

= 1 - 0.2810 using z standard normal probablity table

=0.7190

we get

the probability that the proportion of students who may change their major in the next 2 semesters are more than 115 is 0.7190