Question

the mean yearly rainfall in a city is 146.27 mm with a standard deviation of 75.81 mm. suppose the city received 2.2 mm of rainfall in a year. would this be unusual?

2.2 mm would be unusual since it is more than two standard deviations from the mean.
2.2 mm would be unusual since it is less than two standard deviations from the mean.
2.2 mm would not be unusual since it is less than two standard deviations from the mean.
2.2 mm would not be unusual since it is more than two standard deviations from the mean.

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Explanation:

Step1: Calculate lower and upper bounds

We know that for a normal - distribution, values within 2 standard deviations of the mean are considered usual. The formula for the lower bound $L$ and upper bound $U$ is $L=\mu - 2\sigma$ and $U=\mu+2\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 146.27$ mm and $\sigma = 75.81$ mm.
$L=146.27-2\times75.81$
$U=146.27 + 2\times75.81$

Step2: Calculate the lower bound value

$L=146.27-2\times75.81=146.27 - 151.62=-5.35$

Step3: Analyze the given value

The city received 2.2 mm of rainfall. Since $- 5.35<2.2<146.27 + 151.62$, 2.2 mm is within 2 standard deviations of the mean. So it is not unusual.

Answer:

2.2 mm would not be unusual since it is less than two standard deviations from the mean.