Probability: normal distribution and standard normal random variable

Question

Let $X$ follows the normal distribution $N(1,9)$. Find

$\text{(a)}$ $P(X\le1.4).$

$\text{(b)}$ $P(X\le-1.22).$

$\text{(c)}$ Hence find $P(-1.22\le X\le1.4).$

For $\text{(a)}$, is the answer $0.5530$?

For $\text{(b)}$, is the answer $0.2296$?

For $\text{(c)}$, is the answer $0.3234$?

Find $k$ such that $$P(-k\le Z\le k)=0.97$$ where $Z$ is the standard normal random variable.

For this question, is $k=2.17$?

Answer 1

Yes, indeed, your calculations are all correct! Well done.

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NOTE: However, that being said, the most important thing here is how you arrived at the correct answers. Usually, we can infer from a correct answer that the method used to arrive at it is correct. But not always.

So if you have any questions or doubts about how you arrived at your answers, feel free to elaborate, and I'll get back to you.