Species of shrew normally distributed with a given mean and STD. Please help. The mass of a species of shrew is approximately normally distributed with a mean of **10 grams and STD of 5 grams** , then:!enter image description here A. What is the probability that a random sample of **9 shrews had a total mass of more than 100 grams**? B. What is the probability that a sample of **10 shrews had a mean greater than 12 grams**? I have no idea how to do part A of the problem...? How should I set the problem when I'm looking for a **total mass** of more than 100? Please help. I'm pretty sure my part B of the problem is correct. Does it look right? Thank you so much.

In A. you have two mistakes. Your first mistake is that you have $100-10$ instead of $100-90$ and and your second mistake is that you divided with $\frac{\sigma}{\sqrt{n}}$. But, this is the standard deviation of the mean of the sample, not of the sum of the values of the sample. You should divide with $\sigma \cdot \sqrt{n}$.

Remember that $$S_9=\sum_{i=1}^{9} Y_i \sim N(\mu_9=9\mu, \,\sigma_9^2=9\sigma^2)$$ which for $\mu=10$ and $\sigma=5$ gives $$S_9=\sum_{i=1}^{9} Y_i \sim N(\mu_9=90, \,\sigma_9^2=9\cdot25)$$ So for A. you should have $$\frac{S_9-\mu_9}{\sigma_9}=\frac{100-90}{\sqrt{9\cdot25}}=\frac{10}{15}=0.667$$ and not $54$.