Probability of the sample mean of a Bernoulli

Question

If $X_{1}, X_{2}, ... ,X_{10}$ denotes an independent and identically distributed sample from a Bernoulli(p = 0.4) population distribution. What is the probability that the sample average $X$ equals exactly $0.3\text{?}$ State your answer to three decimal places.

I have simply calculated

Is my procedure correct? Am I missing something?

Thanks you so much guys,

Answer 1

No, that's correct. (You computed the probability that the sum of all 10 was equal to $3$, which is indeed the same as the probability that the sample mean is $3/10$.) If that's homework, you may want to spell this reasoning out, but that's all.

You have made some mistake rounding too early (specifically, the $0.6^7$), however: I personally find $0.215$.

Answer 2

It is correct except for a conceptual mistake in arithmetic that throws off the bottom line, which should be $0.2149908\ldots,$ rounded to $0.215,$ not to $0.216.$

Note: Don't round until the LAST step unless you KNOW what the effect on the bottom line will be.