Suppose that the distribution of weekly water usage for single-family homes in a particular city is approximately normal. The mean is 1400 gallons, and the standard deviation is 300 gallons.
a. What is the z-score for 800 gallons? b. What is the approximate value of the highest 15th percentile?
C. What is the 7-score for 1665 gallons?
d. What is the approximate value of the 14th percentile?
e. What is the percentile for 749 gallons? f. What is the approximate value of the 50th percentile?
Answers
Answer:
Step 1 of 3
The given question deals with the study of the percentile points, for the provided for the data for the weekly water usage.
The data deals with the study of the weekly water usage for single-family homes in a particular city. The data shows, that the mean of the data set is,
The data set is assumed to be normally distributed in nature.
a.
Now, the percentile point is to be obtained. The percentile being considered is, . Thus, as the percentile point is to be obtained, thus the probability to the left of the percentile point has to be, . Now, as the data set is normally distributed in nature, thus the z-score for the probability below the point has to be .
The probability to the left of the z-score is to be . Hence, the corresponding z-score is, obtained as, . Now, we know, that the z-score is obtained by,
Where is the percentile point, and the mean and standard deviation are as provided above.
Hence, the percentile point is obtained as,
Thus, the approximate th percentile point is obtained as, .
Step-by-step explanation:
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