To find the probabilities for the standard normal distribution, we use the cumulative distribution function (CDF) of the standard normal curve.

Solution:

(a) $P(1.32 < z < 2.18)$

$P(1.32 < z < 2.18) = P(Z < 2.18) - P(Z < 1.32)$ Using the standard normal table: $P(Z < 2.18) = 0.9854, \quad P(Z < 1.32) = 0.9066$ $P(1.32 < Z < 2.18) = 0.9854 - 0.9066 = \mathbf{0.0788}$

(b) $P(-1.61 < z < 2.36)$

$P(-1.61 < z < 2.36) = P(Z < 2.36) - P(Z < -1.61)$ From the standard normal table: $P(Z < 2.36) = 0.9909, \quad P(Z < -1.61) = 0.0537$ $P(-1.61 < Z < 2.36) = 0.9909 - 0.0537 = \mathbf{0.9372}$

(c) $P(z > -0.65)$

$P(Z > -0.65) = 1 - P(Z < -0.65)$ From the standard normal table: $P(Z < -0.65) = 0.2578$ $P(Z > -0.65) = 1 - 0.2578 = \mathbf{0.7422}$

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Final Answers:

• (a) $P(1.32 < z < 2.18) = 0.0788$
• (b) $P(-1.61 < z < 2.36) = 0.9372$
• (c) $P(z > -0.65) = 0.7422$

Would you like me to explain any step in more detail?

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Related Questions:

1. How do you calculate probabilities for a normal distribution that is not standard?
2. What is the probability of $P(-2 < z < 1.5)$ in a standard normal curve?
3. How do you find the z-score given a probability?
4. How do you use a standard normal table to find left-tailed probabilities?
5. What is the difference between one-tailed and two-tailed probabilities?

Tip:

If you don't have a z-table handy, you can use statistical software like Excel (NORM.S.DIST function) or a scientific calculator to find cumulative probabilities!