Note: All final answers must be rounded to 4 decimal places of approximation, but do not do any rounding in the middle stages of the solution. A system measured the amount of rain in the same city (in millimeters) for 11 days, returning the following results in ascending order: Amount of rain per day (millimeters): 3.6; 10.3; x; 12.8; 13.3; 14.6; 14.8; 16.1; y; 18.5; z Due to a system error, the values represented by x, y, and z above were not printed. Let q1, q2 and q3 be the quartiles of the sample above. a) it is known that 1.25y-0.75x10.525. Assuming z is an outlier, what is the smallest possible value of z? b) It is assumed from other years that the population variance of the amount of rain in this city is o² = 9.3 . How many days must be analyzed by the system so that the absolute value of the sampling error of the average rainfall is less than 1 unit with a probability greater than or equal to 0.9? c) This system also wants to analyze the proportion p of days in the city whose rainfall amount is less than 10 mm. How many days must be analyzed by the system so that the absolute value of the sample proportion is less than 0.07 units with a probability greater than or equal to 0.99? d) Suppose now that it is estimated that P <= 0.33. What is the sample size to be analyzed in this case to answer the question of the previous item?
Note: All final answers must be rounded to 4 decimal places of approximation, but do not do any rounding in the middle stages of the solution. A system measured the amount of rain in the same city (in millimeters) for 11 days, returning the following results in ascending order: Amount of rain per day (millimeters): 3.6; 10.3; x; 12.8; 13.3; 14.6; 14.8; 16.1; y; 18.5; z Due to a system error, the values represented by x, y, and z above were not printed. Let q1, q2 and q3 be the quartiles of the sample above. a) it is known that 1.25y-0.75x10.525. Assuming z is an outlier, what is the smallest possible value of z? b) It is assumed from other years that the population variance of the amount of rain in this city is o² = 9.3 . How many days must be analyzed by the system so that the absolute value of the sampling error of the average rainfall is less than 1 unit with a probability greater than or equal to 0.9? c) This system also wants to analyze the proportion p of days in the city whose rainfall amount is less than 10 mm. How many days must be analyzed by the system so that the absolute value of the sample proportion is less than 0.07 units with a probability greater than or equal to 0.99? d) Suppose now that it is estimated that P <= 0.33. What is the sample size to be analyzed in this case to answer the question of the previous item?
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.6: Wind And Water Current Problems
Problem 10P
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Transcribed Image Text:Note: All final answers must be rounded to 4 decimal places of approximation, but do not do any rounding
in the middle stages of the solution.
A system measured the amount of rain in the same city (in millimeters) for 11 days, returning the following
results in ascending order:
Amount of rain per day (millimeters): 3.6; 10.3; x; 12.8; 13.3; 14.6; 14.8; 16.1; y; 18.5; z
Due to a system error, the values represented by x, y, and z above were not printed.
Let q1, q2 and q3 be the quartiles of the sample above.
a) It is known that 1.25y – 0.75x > 10.525 Assuming z is an outlier, what is the smallest possible
value of z?
b) It is assumed from other years that the population variance of the amount of rain in this city is o? = 9.3
. How many days must be analyzed by the system so that the absolute value of the sampling error of the
average rainfall is less than 1 unit with a probability greater than or equal to 0.9?
c) This system also wants to analyze the proportion p of days in the city whose rainfall amount is less than
10 mm. How many days must be analyzed by the system so that the absolute value of the sample
proportion is less than 0.07 units with a probability greater than or equal to 0.99?
d) Suppose now that it is estimated that P <= 0.33 What is the sample size to be analyzed in this case to
answer the question of the previous item?
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