Find the length of the arc shown in brown. Leave your answer in terms of pi.
2 answers:
The central angle that captures the brown arc is 120°. To find out what fraction of the total circumference the brown arc is, we can find the ratio of this 120° angle to the total central angle of a circle, which is 360°. So we have:
Now we know the brown arc is
of the total circumference. The circumference is π*diameter, so in this case it’s 24π.
Finally, we do:
Now we know the brown arc is
Finally, we do:
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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.