The average rainfall in x city for the month of March is 9.22 centimeters. Assuming a normal distribution with a standard deviation of 2.83 centimeters. Find the probability that the next march city x receives less than 1.84 centimeters of rain, more than 5.00 centimeters but not over 7 centimeters of rain and more than 13.8 centimeters

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The average rainfall in x city for the month of March is 9.22 centimeters. Assuming a normal distribution with a standard deviation of 2.83 centimeters, the required probabilities can be determined using a normal distribution table.

To find the probability that the city receives less than 1.84 centimeters of rain, the area below the z-score for 1.84 is required. The z score for 1.84 is (9.22 - 1.84)/2.83 = 2.6077. The corresponding value for the probability is (0 - 0.9953) = 0.47%

The z-score for values of rainfall more than 5.00 centimeters but not over 7 centimeters of rain is the area between a z score of (9.22 - 7)/2.83 = 0.7844 and (9.22 - 5)/2.83 = 1.4911. The corresponding probability is: 0.9319 - 0.7823 = 14.96%

The z-score for a value of 13.8 centimeters is (9.22 - 13.8)/2.83 = -1.618. The probability for rainfall above 13.8 centimeters is 1 - 0.9463 = 5.32%

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