Questions: Find the z-scores that correspond to the percentage of adult spiders that have carapace lengths between 17 mm and 18 mm The percentage of adult spiders that have carapace lengths between 17 mm and 18 mm is equal to the area under the standard normal curve between -1.79 and -1.16. (Round to two decimal places as needed) Find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 22 mm. The percentage of adult spiders that have carapace lengths exceeding 22 mm is equal to the area under the standard normal curve that lies to the right of (Round to two decimal places as needed)

Find the z-scores that correspond to the percentage of adult spiders that have carapace lengths between 17 mm and 18 mm

The percentage of adult spiders that have carapace lengths between 17 mm and 18 mm is equal to the area under the standard normal curve between -1.79 and -1.16. (Round to two decimal places as needed)

Find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 22 mm.

The percentage of adult spiders that have carapace lengths exceeding 22 mm is equal to the area under the standard normal curve that lies to the right of (Round to two decimal places as needed)

Transcript text: Find the $z$-scores that correspond to the percentage of adult spiders that have carapace lengths between 17 mm and 18 mm The percentage of adult spiders that have carapace lengths between 17 mm and 18 mm is equal to the area under the standard normal curve between -1.79 and -116 . (Round to two decimal places as needed) Find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 22 mm . The percentage of adult spiders that have carapace lengths exceeding 22 mm is equal to the area under the standard normal curve that lies to the right of $\square$ (Round to two decimal places as needed)

Solution

Solution Steps

Step 1: Calculate Z-scores for Carapace Lengths

To find the z-scores corresponding to the percentage of adult spiders that have carapace lengths between $ 17 \, \text{mm} $ and $ 18 \, \text{mm} $, we use the given z-scores of $ -1.79 $ and $ -1.16 $.

The results indicate that the area under the standard normal curve between these z-scores corresponds to the percentage of spiders with carapace lengths in this range. The calculated probability for this range is $ 0.09 $.

Step 2: Calculate Z-score for Carapace Length Exceeding 22 mm

Next, we find the z-score for the carapace length of $ 22 \, \text{mm} $. The calculated z-score is $ 22.0 $. This indicates that a carapace length of $ 22 \, \text{mm} $ is $ 22 $ standard deviations above the mean of the distribution.

Final Answer

For part d, the z-scores corresponding to the carapace lengths between $ 17 \, \text{mm} $ and $ 18 \, \text{mm} $ are $ z_{start} = -1.79 $ and $ z_{end} = -1.16 $ with a probability of $ 0.09 $.

For part e, the z-score corresponding to the carapace length exceeding $ 22 \, \text{mm} $ is $ z = 22.0 $.

Thus, the final answers are: \[ \boxed{z_{start} = -1.79, \, z_{end} = -1.16, \, z = 22.0} \]

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