Statistics Hypothesis test on a single sample

Question

I'm revising for my statistics exam that's coming up but I have a few questions without solutions in the book. I've worked out an answer however I'm not sure if it's correct. This question is:

In order for a clothes washer to qualify for ENERGY STAR, it must have a Modified Energy Factor (MEF, a dimensionless quantity) of 1.42 or greater. Thirty-eight Speed Queen commercial washers were selected at random, and the MEF for each was measured. The sample mean was x = 1,228. Assume the distribution of MEF is normal and σ = 0.5. Conduct a hypothesis test to determine whether there is any evidence the mean MEF of this Speed Queen washer is less than 1.42. Use α = 0.01.

So my first step was to declare the variables from the question:
H0 = μ = 1.42
Ha = μ < 1.42
x̅ = 1.228
σ = 0.5
α = 0.01
Then I put that in the z score formula:
z = x̅ - H0 / (σ/sqrt(n))
z = 1.228 - 1.42 / (0.5/sqrt(38))
z = -2.367
Now I can look up the z table for a p value of p = 0.0091
Then I conclude that I reject the null hypothesis because the p value is < than alpha the level of significance; 0.0091 < 0.01.
Is this the correct answer/approach?