Question

the deaths attributed to uv radiation have a mean of 168.4 with a standard deviation of 108.7. suppose in a given year there were 588 deaths attributed to uv radiation in a country. is this value unusual? 588 deaths would not be unusual since it is more than two standard deviations from the mean. 588 deaths would be unusual since it is less than two standard deviations from the mean. 588 deaths would be unusual since it is more than two standard deviations from the mean. 588 deaths would not be unusual since it is less than two standard deviations from the mean.

Explanation:

Step1: Calculate the range for non - unusual values

Non - unusual values are within $z=- 2$ and $z = 2$ standard deviations from the mean. The formula for a value $x$ in terms of the mean $\mu$ and standard deviation $\sigma$ and z - score is $x=\mu+z\sigma$. For $z = - 2$, $x_1=\mu-2\sigma$, and for $z = 2$, $x_2=\mu + 2\sigma$. Given $\mu = 168.4$ and $\sigma=108.7$.
$x_1=168.4-2\times108.7=168.4 - 217.4=-49$
$x_2=168.4 + 2\times108.7=168.4+217.4 = 385.8$

Step2: Check if the given value is within the range

The given value is $x = 588$. Since $588>385.8$, it is more than two standard deviations from the mean. Values more than two standard deviations from the mean are considered unusual.

Answer:

588 deaths would be unusual since it is more than two standard deviations from the mean.