Population proportion *statistics*

[georgeh]

Homework Statement

Harley-Davidson motorcyles make up 14% of all the motorcyles registered in the United States. You plan to interview an SRS of 500 motorcyle owners.
a) what the approximate distribution of the proportion of your sample who owns harleys?
b) Is your sample likely to contain 20% or more who own Harleys? Is it likely to contain at least 15% Harley owners? Do normal probability calculations to answer these questions

Homework Equations

p-phat = count of success in the sample/n
p = mean of the sampling distribution
z =( p-hat - p)/ std.dev

The Attempt at a Solution

I believe p = .14. n = 500
I don't understand what is meant by "approximate distribution of the proportion of your sample who owns harleys".
If they mean p-hat, would p-hat =(500*14/100) / 500 ? bit that would give me .14..

 

[AlephZero]

Hint: The question says "Do normal probability calculations to answer these questions".

The "exact" probability distribution here is a Binomial distribution. How do you use a Normal distribution to approximate a Binomial distribution?