To the left of z=−0.75 15

The Correct Answer and Explanation is:

Correct Answers

14. To the left of z = -0.75 → 0.2266
15. Between z = 1.09 and z = 1.83 → 0.4664 − 0.3621 = 0.1043
16. Between z = 1.23 and z = 1.90 → 0.4713 − 0.3907 = 0.0806
17. Between z = -1.77 and z = -1.46 → 0.0721 − 0.0721 = 0.0000 (Note: This question may contain a typo as both z-scores are the same when reversed)
18. Between z = -0.96 and z = -0.36 → 0.3594 − 0.1700 = 0.1894
19. Between z = -1.98 and z = -1.46 → 0.0721 − 0.0239 = 0.0482
20. Between z = -1.12 and z = 0.24 → 0.5948 − 0.1314 = 0.4634
21. To the left of z = 1.12 → 0.8686
22. To the left of z = 1.31 → 0.9049
23. To the right of z = -0.18 → 1 − 0.4286 = 0.5714
24. To the right of z = -1.92 → 1 − 0.0274 = 0.9726
25. To the right of z = 1.92 and to the left of z = -0 → 1 − 0.9726 + 0.5 = 0.5274

Explanation

In statistics, a z-score tells us how many standard deviations a value lies from the mean in a normal distribution. The standard normal distribution is symmetrical, bell-shaped, and centered at a mean of zero.

The area under the curve represents probabilities. To solve these problems, we refer to a Z-table which gives cumulative probabilities from the far left up to a specific z-score. For questions that ask for the probability “to the left of z,” we directly read the cumulative value. For areas “to the right,” we subtract the cumulative value from one. When asked for areas between two z-scores, we subtract the smaller cumulative probability from the larger one.

This technique is essential in hypothesis testing, quality control, and any context where understanding deviation from a population mean is vital. Mastery of this method helps build deeper statistical intuition.