To solve these questions, I’ll provide the calculations for the missing values using the standard normal distribution (z-scores).

Here's how to approach each part:

1. (a) Given $\text{Area to the left of } z = 0.9750$

   • The z-score for an area of 0.9750 is approximately 1.96, which you already have correct.

2. (b) Given $\text{Area between } 0 \text{ and } z = 0.4750$

   • The area between 0 and z being 0.4750 implies that the area to the left of z is $0.5 + 0.4750 = 0.9750$.
   • For an area of 0.9750 to the left, the corresponding z-score is 1.96.

3. (c) Given $\text{Area to the left of } z = 0.7357$

   • The z-score for an area of 0.7357 is approximately 0.63, which is marked correct.

4. (d) Given $\text{Area to the right of } z = 0.1251$

   • Area to the right of z being 0.1251 implies the area to the left is $1 - 0.1251 = 0.8749$.
   • The z-score for an area of 0.8749 to the left is approximately 1.15.

5. (e) Given $\text{Area to the left of } z = 0.6293$

   • The z-score for an area of 0.6293 is approximately 0.33.

6. (f) Given $\text{Area to the right of } z = 0.3707$

   • Area to the right of z being 0.3707 implies the area to the left is $1 - 0.3707 = 0.6293$.
   • The z-score for an area of 0.6293 to the left is approximately 0.33.

Summary of Correct Answers

• (a) 1.96
• (b) 1.96
• (c) 0.63
• (d) 1.15
• (e) 0.33
• (f) 0.33

Would you like further explanation on any part?

Related Questions to Explore:

1. What is the significance of z-scores in statistics?
2. How do you interpret areas under the standard normal curve?
3. What are common z-scores and their corresponding areas?
4. How would you use z-scores in hypothesis testing?
5. Can z-scores be negative, and what does a negative z-score mean?

Tip:

When working with z-scores, always double-check the area to ensure if it's to the left or right of the z-score, as this changes the interpretation.