I have this problem that I've been working on that I believe I am approaching wrong. It goes like (shortened for brevity): There is a house for sale and the owners expected 15 offers. The offers are normally distributed and have a mean of 10 and a standard deviation of 3.2
I used the NORM.INV(Rand(), 10, 3.2) function in excel 15 times (because of the 15 offers). I got the random values. However the question asks:
- estimate the distribution of the minimum bid
- estimate the expected value of the minimum bid
I don't understand what it is asking when it says "distribution of the minimum bid". Because the minimum bid in the sample is only going to be the lowest randomly generated value correct? The expected value is simply the value of the lowest randomly generated offer correct?
What am I missing here? Thank you!
I believe what the question is asking for is this: take a sample of $n$ offers and find the minimum value of that sample. Then do it again with a new sample of size $n$. And again. And again...
What you are essentially doing is looking at the Sampling Distribution of the data. It's very common to look at the Sampling Distribution to begin making statistical inferences, such as hypothesis testings and confidence intervals.
For your particular case, it appears they want you to find the sampling distribution of the minimum value of a sample of fixed size $n$, which is free for you to choose, but you will get more accurate results the larger the $n$. Using the normal distribution given, run it a few times and get some samples down and then take the minimum value from each sample and see if there is any trend with them. Do they seem to be "close" to one another? Does their distribution appear normally distributed, or bell shaped, as well?