A sample of temperatures from a dolphin pool at Mystic Aquarium was found to be
ID: 3152987 • Letter: A
Question
A sample of temperatures from a dolphin pool at Mystic Aquarium was found to be normally distributed with a mean of 72.4 degrees (F) and a standard devlation of 2 6 decrees (F). Represent the data with a normal curve and label the horizontal axis in standard deviation units. Then use the Empirical Rule to fill in the areas. Approximately what percentage of the time are the temperatures in the pool greater than 75 degrees? below 67.2 degrees? Between 67.2 and 77.6 degrees? Between 67.2 and 75 degrees? Above 76 degrees? (You can only guess at this one!!) If a temperature above 77.6 is unacceptable (too warm), what percent of the time is the temperature too warm?Explanation / Answer
a)
Note that 75 degrees is 1 standard deviation above the mean.
Hence, by 68-95-99.7 rule, the upper tail is
P(x>75) = (100-68)/2 = 16% [ANSWER]
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b)
Note that 67.2 degrees is 2 standard deviations below the mean.
Hence, by 68-95-99.7 rule, the lower tail is
P(x<67.2) = (100-95)/2 = 2.5% [ANSWER]
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c)
Note that 67.2 and 77.6 degrees are 2 standard deviations below and above the mean.
Hence, by 68-95-99.7 rule,
P(67.2<x<77.6) = 95% [ANSWER]
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d)
Note that 67.2 degrees is 2 standard deviations below the mean.
Note that 75 degrees is 1 standard deviation above the mean.
Hence, by 68-95-99.7 rule, from parts 1 and 2,
P(67.2<x<75) = 100% - 16% - 2.5% = 81.5% [ANSWER]
e)
As 76 is between 1 and 2 standard deviations above the mean, then between 2.5% and 16% is above 76 degrees. So likely, it is around 10%. [ANSWER]
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e)
Note that 77.6 degrees is 2 standard deviations above the mean.
Hence, by 68-95-99.7 rule, the upper tail is
P(x>77.6) = (100-95)/2 = 2.5% [ANSWER]
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