Probability Type I error I have these values:
A sample of size $100$ is taken from the population.
Standard Deviation is $5$.

Average is $125$.
$H_0$: $\mu =125$ Against $H_a$: $\mu <125$
Accept $H_0$ if the sample mean is $\bar{\mathbb{x}} ≥ 124$
Reject $H_0$ if the sample mean  $\bar{\mathbb{x}} < 124 $
Find the probability of making a Type I error.

I did:
Variance$\; =25$, because S.D. is $5$ then, 
$$Z= \frac{\bar{\mathbb{x}} -\mu}{\text{S.D.}/\sqrt{100}}$$ 
which is : $ Z=\frac{124-125}{5/10}=-2 $
$1- \Phi (-2)=1-0.97725=0.023$
The probability of making a type I error is $2.3%$.
Am I correct? Can anyone let me know if this is correct?
thanks

You work seems fine, except for the final step as Augustin pointed out.
In terms of probability, recall that we are seeking the probability that $\bar x < 124$ given that the $\mu = 125$. This means
$$P(\bar x <124|\mu = 125)$$
By standardizing, we get
\begin{align*}
P(\bar x <124|\mu = 125) &= P\left(Z < \frac{124-125}{5/\sqrt{100}}\bigg|\mu
= 125\right) \\
&= P(Z<-2|\mu = 125) \\
&= \Phi(-2) \\
&= 0.02275013
\end{align*}
In simpler terms (if you don't know probability), we are looking for the "area to the left" of $-2$ under the normal curve.
