Need help starting this question; unable to identify what type of question it is

[carletonUstudent]

I can't tell if its asking for a binomial distribution or a normal probability distribution.. or maybe an approximation of a binomial distribution using a normal distribution..but then where does a random variable come in?

here is the question:

A company that manufactures mufflers for cars offers a lifetime warranty on its products provided that ownership of the car does not change. Suppose that only 20% of its mufflers are replaced under this warranty.

a) Define the random variable X as the number of mufflers replaced in a sample of 400 purchases. Give the distribution of X.
b)Referring to part 5a), what is the approximate probability that between 75 and 100 mufflers (inclusive) are replaced under warranty?

 

[hlsmith]

Seems like binomial to me. You have no mean, std dev, etc. Just a binary event.

 

[emekadavid]

Binomial.
A = {Mufflers replaced under warranty}
B = {Mufflers not replaced under warranty}
Binomial to me.

 

[dcasmr]

Binomial.
A = {Mufflers replaced under warranty}
B = {Mufflers not replaced under warranty}
Binomial to me.

Hello,
You can solve this using the Binomial distribution or the normal distribution. Under certain conditions, when np > 5 and nq > 5 (which is the case here), you can use the Normal approximation to the binomial distribution . Try solving it using both approach and you will find that the answers are pretty close.
Thanks,
Luke