Use the empirical rule to solve the problem. The annual precipitation for one city is normally distributed with a mean of 288 inches and a standard deviation of 3.7 inches. Fill in the blanks. In 95.44% of the years, the precipitation in this city is between ___ and ___ inches. Round your answers to the nearest tenth as needed.

And if we solve for a we got

And the limits for this case are: (214.4; 295.4)

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the annual precipitation of a population, and for this case we know the distribution for X is given by:

Where and

The confidence level is 95.44 and the signficance is and the value of . And the critical value for this case is

Using this condition we can find the limits

And if we solve for a we got

And the limits for this case are: (214.4; 295.4)

the answer will be

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