What a terrible question! None of the options is really ruled out by the wording*. (It's clear enough what answer they probably want, but that's really beside the point here)
* though I can rule one out from other considerations ... but in a way that would invalidate the choices they'd no doubt want you to pick on other questions of this type/
Let me show you why:
"Scientists are weighing frogs" ... this tells us we're dealing with a sample,
"The mean weight is 5.5oz and the median weight is 4.1oz." ... sample mean > sample median
That's the information. Nothing about sample size. No definition of what 'few' or 'many' not 'heavy' or 'light' mean in this context.
I know it can't be choice A because median=mean=mode for a normal distribution.
For a population. This is a sample. You can easily get samples where mean and median differ. Imagine we have a sample of size 3 where the weights are 4.09, 4.10 and 8.31 oz. If the population mean was 5.5 and the population standard deviation was somewhere near 1.5, this wouldn't be a surprising outcome.
So no, that information doesn't rule out option A
Can't be choice B either because this is usually modeled for waiting times.
So? How does what people often choose to a distribution for rule it out as a possibility?
If it were the case that we had the population mean and median, those values would rule out an exponential distribution (since for an exponential the median should be $\mu\ln 2$ and it's bigger than that), but again, these are sample figures.
Can't be choice C because median is less than 5.5oz.
Again, so? What if a proportion of $0.5+\epsilon$ are around 4.1 oz and a proportion of $0.5-\epsilon$ are around 6.9 oz?
The problem is that without some kind of precise definition of 'few' or 'many', 'heavy' or 'light' in this context, you can't rule out C or D.
[We might argue from biology that the exponential is unlikely (since it implies that the most likely sizes are very small). We could use biological arguments to rule out the normal (frogs don't have negative weights, so they can't be exactly normal). We still can't choose between C and D.]