A rope is used to tie a boat to a dock. The angle of depression from the boat to the ocean floor directly beneath the dock is 40
degrees. The boat is 25.17 feet above the ocean floor.
What is the length of the rope between the boat and the dock?
What is the length of the rope between the boat and the dock?
1 answer:
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Answer:
For the 99th percentile, we have X = 206 seconds.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
99th percentile:
Value of X when Z has a pvalue of 0.99. So we use
For the 99th percentile, we have X = 206 seconds.