Using the standard normal distribution find the following. (a) P (z < 1. 24) (b) P(z > –2. 81) (c)P (-2.81 < z < 2. 51) (d) Find Z^so that (d) P (–2* < z < z*) = 0. 96

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**Understanding the Standard Normal Distribution**

Using the standard normal distribution, find the following probabilities:

(a) \( P(z \leq 1.24) \)

(b) \( P(z \geq -2.81) \)

(c) \( P(-2.81 \leq z \leq 2.51) \)

(d) Find \( z^* \) so that:

   \( P(-z^* \leq z \leq z^*) = 0.96 \)

**Explanation:**

You need to use a standard normal distribution table or calculator to find the probabilities for parts (a), (b), and (c).

For part (d), you will find the value of \( z^* \) such that the probability between \(-z^*\) and \(z^*\) is 0.96. This involves finding the z-scores that correspond to the middle 96% of the distribution.
Transcribed Image Text:**Understanding the Standard Normal Distribution** Using the standard normal distribution, find the following probabilities: (a) \( P(z \leq 1.24) \) (b) \( P(z \geq -2.81) \) (c) \( P(-2.81 \leq z \leq 2.51) \) (d) Find \( z^* \) so that: \( P(-z^* \leq z \leq z^*) = 0.96 \) **Explanation:** You need to use a standard normal distribution table or calculator to find the probabilities for parts (a), (b), and (c). For part (d), you will find the value of \( z^* \) such that the probability between \(-z^*\) and \(z^*\) is 0.96. This involves finding the z-scores that correspond to the middle 96% of the distribution.
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