What is the probability of obtaining a sample proportion less than 0.30?

Question

It is known that the population proportion of BYU-Idaho students that go cross country skiing at least once winter semester is p = 0.38. Suppose a random sample of size n = 80 BYU-Idaho students is selected, and the proportion of the sample that go cross country skiing is calculated. What is the probability of obtaining a sample proportion less than 0.30?

Answer 1

Hello Kar,

What you are needing to do is calculate z score for a standard proportion. This is slightly different than your traditional z score calculation because it is a proportion and not a continuous value. You can use the following formula below:

z = (p-p₀) / σ

σ= √(p₀(1-p₀)/n)

1. p = observed sample proportion
2. p₀ = hypothesized population proportion
3. n = sample size

You can then take your z value and plug it into a calculator or z score table to determine the probability. It should be about 0.07