Question

the mean yearly rainfall in a city is 130.46 mm with a standard deviation of 66.41 mm. suppose the city received 176.9 mm of rainfall in a year. would this be unusual?

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

Explanation:

Step1: Calculate z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 176.9$ (observed value), $\mu=130.46$ (mean), and $\sigma = 66.41$ (standard deviation). So, $z=\frac{176.9 - 130.46}{66.41}=\frac{46.44}{66.41}\approx0.7$.

Step2: Determine if it's unusual

In a normal distribution, values within about 2 standard deviations of the mean are considered usual. Since $|z| = 0.7<2$, the value is not unusual.

Answer:

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