Let's calculate each of the probabilities based on the standard normal distribution $Z$, where $Z$ has a mean $\mu = 0$ and standard deviation $\sigma = 1$. We'll use the cumulative distribution function (CDF) of the standard normal distribution.

(a) $P(Z > 2.00)$

• To find this probability, we calculate $P(Z > 2.00)$. Using the CDF for $Z = 2.00$, we find the area to the left of 2.00 and subtract it from 1.

  $P(Z \leq 2.00) \approx 0.9772$ Therefore, $P(Z > 2.00) = 1 - 0.9772 = 0.0228$

  Answer: $P(Z > 2.00) \approx 0.023$

(b) $P(Z \leq 1.44)$

• Here, we need the cumulative probability for $Z \leq 1.44$.

  $P(Z \leq 1.44) \approx 0.9251$

  Answer: $P(Z \leq 1.44) \approx 0.925$

(c) $P(-1.09 < Z < 2.20)$

• This is the probability that $Z$ lies between $-1.09$ and $2.20$. We calculate:

  $P(Z \leq 2.20) \approx 0.9861$ $P(Z \leq -1.09) \approx 0.1379$ Therefore, $P(-1.09 < Z < 2.20) = 0.9861 - 0.1379 = 0.8482$

  Answer: $P(-1.09 < Z < 2.20) \approx 0.848$

Let me know if you'd like further details on these calculations or have any questions!

---

Here are 8 related questions you might find interesting:

1. What is $P(Z > 1.96)$?
2. How do you calculate $P(Z < -1.64)$?
3. What is the probability that $Z$ lies between 0 and 2.33?
4. How do you interpret a z-score of 3.0 in terms of probability?
5. What is $P(-0.5 < Z < 0.5)$?
6. How do you find the area under the curve to the right of $Z = -1.5$?
7. What is the 90th percentile of the standard normal distribution?
8. How do you standardize a variable to calculate probabilities?

Tip: Always remember that the total area under the standard normal curve equals 1, so probabilities for values outside a given range can often be easily calculated by subtracting from 1.