Question
In: Statistics and Probability
The per capita energy consumption level (in kilowatt-hours) in a certain country for a recent year...
The per capita energy consumption level (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure.
Mean=2296
Standard deviation=581.8
(a) What consumption level represents the 5 th percentile?
(b) What consumption level represents the 17 th percentile?
(c) What consumption level represents the third quartile?
Solutions
Expert Solution
Solution: We are given:
(a) What consumption level represents the 5th percentile?
Answer: To find the consumption level that represents the 5th percentile, we need to find the z-value corresponding to area 0.05. Using the standard normal table, we have:
Now using the z-score formula, we have:
Therefore, the consumption level that represents 5th percentile is 1338.939
(b) What consumption level represents the 17th percentile?
Answer: To find the consumption level that represents the 17th percentile, we need to find the z-value corresponding to area 0.17. Using the standard normal table, we have:
Now using the z-score formula, we have:
Therefore, the consumption level that represents 17th percentile is 1740.963
(c) What consumption level represents the third quartile?
Answer: To find the consumption level that represents the third quartile, we need to find the z-value corresponding to area 0.75. Using the standard normal table, we have:
Now using the z-score formula, we have:
Therefore, the consumption level that represents the third quartile is 2688.133
orchestra answered 1 year agoRelated Solutions
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