Find the z-scores for which 15% of the distribution's area lies between -z and z. The z-scores are ◻. (Use a comma to separate answers as needed. Round to two decimal places as needed.)

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Understand the problem: Understand the problem. We need to find two z-scores such that the area between them under the standard normal distribution curve is 15%. Since the normal distribution is symmetric, the area from -z to z will be split equally on both sides of the mean (which is 0 for a standard normal distribution). This means that 7.5% of the area lies to the left of -z and 7.5% to the right of z.Use the standard normal distribution table: Use the standard normal distribution table. To find the z-scores, we will use the standard normal distribution table, which gives us the area to the left of a given z-score. Since we want 7.5% (or 0.075) of the area to the left of -z, we need to find the z-score that corresponds to an area of 0.5 - 0.075 = 0.425 to the left of it.Look up the z-score: Look up the z-score corresponding to an area of 0.425. Using the standard normal distribution table, we find that the z-score that leaves an area of 0.425 to its left is approximately -1.44. This is the z-score for -z.Find the positive z-score: Find the positive z-score. Since the normal distribution is symmetric, the positive z-score +z that leaves an area of 0.575 to its left (0.5 + 0.075) will have the same absolute value as -z. Therefore, +z is also approximately 1.44.Verify the solution: Verify the solution. We have found that the z-scores are approximately -1.44 and 1.44. To verify, we can check that the area between these z-scores is 15%. The area to the left of 1.44 is 0.575, and the area to the left of -1.44 is 0.425. The difference between these areas is 0.575 - 0.425 = 0.15, which is 15%. This confirms that our z-scores are correct.

Find the $z$ -scores for which $15 \%$ of the distribution's area lies between $-z$ and $z$ . $\newline$ The $z$ -scores are $\square$ . $\newline$ (Use a comma to separate answers as needed. Round to two decimal places as needed.)

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Find the z z z-scores for which 15% 15 \% 15% of the distribution's area lies between −z -z −z and z z z.\newlineThe z z z-scores are □ \square □.\newline(Use a comma to separate answers as needed. Round to two decimal places as needed.)

Find the $z$ -scores for which $15 \%$ of the distribution's area lies between $-z$ and $z$ . $\newline$ The $z$ -scores are $\square$ . $\newline$ (Use a comma to separate answers as needed. Round to two decimal places as needed.)