A cylindrical water bottle has a diameter of 2.5 inches and a height of 12 inches. The water surface 2.5 inches from the top. To
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Answer:
Upper P95 = 16.21in
Step-by-step explanation:
When the distribution is normal, we use 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 question, we have that:
Upper P 95
This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
Then
Upper P95 = 16.21in