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I think my question has a really simple answer, but I’d still really appreciate your help :)

I’m given that a distribution is negatively skewed with a mean of 55 and a variance of 15, and then am asked: for a random sample of n=80, what is the probability that X is less than 54 and X is between 54 and 58.

I know how to go about this if it was normally distributed which would be to find the expected value of m and then the z-score. I’m wondering if that would be the same for a distribution that is negatively skewed.

Thank you!

Iplaysoccer
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    There are an infinite number of negatively skewed distributions sharing the same mean and variance, and thus it is logically impossible to give an answer without knowing the precise distribution at hand. – David G. Stork Apr 19 '23 at 02:20
  • What's the context here - are you sure it's not a question about the probabilities of $\mu_x$, and the information you're given isn't sample mean and sample variance? Because then you can apply the central limit theorem, which would allow you to do what you're thinking of with a normal distribution and a Z-score. – Amaan M Apr 19 '23 at 03:51

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