# Thread: help me....

1. ## help me....

According to a 1997 study, 29.3% of self-employed persons worked on their home based businesses 35 hours or more each week. What is the probability that at least 30.5% of 800 people randomly sampled from the study’s population worked on their businesses no less than 35 hours each week in 1997?

2. Originally Posted by het_490@yahoo.com
According to a 1997 study, 29.3% of self-employed persons worked on their home based businesses 35 hours or more each week. What is the probability that at least 30.5% of 800 people randomly sampled from the study’s population worked on their businesses no less than 35 hours each week in 1997?
Let X be the random variable number of people who worked on their home-based businesses for 35 hours or more.

Then X ~ Binomial(n = 800, p = 0.293)

30.5% of 800 is equal to 244.

So you want Pr(X \geq 244).

It'd be reasonable to use the normal approximation to the binomial distribution here (why?). But why bother if you can access a standard machine like a TI-89 that can crank out an answer in short order.