I am studying for the exam on Probability and I have some questions about Standard Normal Distribution.
In particular I am solving an exercise and I don't know if I am solving it correctly.
The exercise is this:
There is a machine that fills jars to a weight that is normally distributed with mean 400g and a standard deviation 4g.
a) What is the probability that a jar will be at least 410g?
b) What is the probability that 2 jars will be at least 822g?
I solved like this:
a) $Z = \frac{X - \mu}{\sigma} = \frac{410 - 400}{4} = \frac{10}{4} = 2.5$ Now, looking at the Distribution Table, I see that
$Pr[X>410] = 1 - 0.9938 = 0.0062$
b) $Z = \frac{X - \mu}{\sigma} = \frac{822 - 800}{8} = \frac{11}{4} = 2.75$
Now, looking at the Distribution Table, I see that
$Pr[X>822] = 1 - 0.9970 = 0.003$
Is my solution correct?