Bob's z-score for the last exam was 1.52 in Prof. Axolotl's class BIO 417, "Life Cycle of the Ornithorhynchus." Bob said, "Oh, g
ood, my score is in the top 10 percent." Assuming a normal distribution of scores, is Bob right?
1 answer:
Answer:
yes
Step-by-step explanation:
The 90-th percentile of a normal distribution corresponds to a z-score of 1.282. Bob's z-score is above that, so he is definitely in the top 10%.
_____
If you haven't memorized the percentiles associated with the normal distribution, it is convenient to use a calculator or table of values.
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Answer:
25.61 feet
Step-by-step explanation:
First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.
Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.
One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have
sin(80°) = opposite / 26 feet
multiply both sides by 26 feet
sin(80°) * 26 feet = opposite
= 25.61 feet as the height of the wall the ladder reaches
