# Find probability that a newborn weighs between $6$ and $8$ pounds; given mean and standard deviation but not given sample size

The weight of a newborn baby randomly sampled from a particular population of babies is known to be normally distributed with a population mean weight of $7.25$ pounds and a population standard deviation of $2$ pounds.

If a baby is randomly sampled from this population, what is the probability that the baby weighs between $6$ and $8$ pounds?

Normally I am used to solving them by using $\frac{\bar{X}-\mu}{\sigma / \sqrt{n}}$ and plugging in $6$ and $8$ and finding the values with the chart, but I am not given $n$ (sample size) in this problem. So is this problem not solvable since there is not enough information or is there another approach to finding the answer?

• "A (single) baby is sampled from population..." – Zoran Loncarevic Feb 15 '16 at 17:06

You are not looking for $$P(6 < \bar X <8)$$ since this generally for a larger sample sizes, meaning $n\geq 2$. You are looking for $$P(6<X<8),$$ which I guess you could say $n = 1$.
You can check to see that the final answer is $0.3801842$.