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

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.

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