Math Help - (Intro Stats) Standard Normal Distribution

1. (Intro Stats) Standard Normal Distribution

Can someone help me with this question?

 The average age of doctors in a certain hospital is 43.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 8.0 years. If 25 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 43.8 years. Assume that the variable is normally distributed.

2. Re: (Intro Stats) Standard Normal Distribution

Let $Y = (X_1 + X_2 + ... + X_{25})/25$ be the average age of 25 doctors where $X_i$ is the age of a randomly selected doctor. If $X_i$ is normally distributed then so is $Y$.

$Y$ will be distributed as follows: $Y \sim N\left(43, \left(\frac{8}{\sqrt{25}}\right)^2 \right)$ (mean, variance)