probability, normal distribution mean

Question

Should I use a certain table for this question or should I use a special formula. A random value has a normal distribution with the mean 102.9 and the standard deviation 4.7. What are the probabilities that this random variable will also take on a value

a. Less than 110.1;

b. Greater than 95.6;

c. Between 104.5 and 105.9;

d. Between 98.7 and 150?

I have worked so far by finding the z value and im going on to find it through the table.

Answer 1

the formula for $P(X \leq x)$ is $\Phi\left( \frac{x-\mu}{\sigma} \right)$

And for $P(X \geq x)=1-\Phi\left( \frac{x-\mu}{\sigma} \right)$

And for $P(x_1 \leq X \leq x_2)=\Phi\left( \frac{x_2-\mu}{\sigma} \right)-\Phi\left( \frac{x_1-\mu}{\sigma} \right)$

$\Phi(.)$ is the function of the normal distribution.

greetings,

calculus