Question

It has been estimated that 26% of all university students switch majors within their first two years of starting classes. If a random sample of 560 third-year students is taken at a city university, what is an estimate of the probability that 23% or less had switched majors within their first two years? Use Appendix B.1 for the z-values. (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Probability

Answer 1

Solution:
Given in the question
P(university students switch majors within their first two years of starting classes) = 0.26
Number of sample(n) = 560
We need to calculate the probability that 23% or less had switched majors within their first two years i.e. P(p^<=0.23)=?
Here we will use the standard normal distribution, First, we will calculate Z-score which can be calculated as
Z-score = (p^-p)/sqrt(p*(1-p)/n) = (0.23-0.26)/sqrt(0.26*(1-0.26)/560) = -0.03/0.0185 = -1.62
From Z table we found a p-value
P(p^<=0.23) = 0.0526
So there is a 5.26% probability that 23% or less had switched majors within their first two years.