Question

the times for the passage of play in a rugby game have a mean of 17.91 seconds with a standard deviation of 11.86 seconds. suppose a passage of play in a rugby game takes 28.2 seconds. would it be unusual for this to happen? 28.2 would not be unusual since it is less than two standard deviations from the mean. 28.2 would be unusual since it is more than two standard deviations from the mean. 28.2 would not be unusual since it is more than two standard deviations from the mean. 28.2 would be unusual since it is less than two standard deviations from the mean.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 28.2$ (the value in question), $\mu=17.91$ (the mean), and $\sigma = 11.86$ (the standard deviation).
$z=\frac{28.2 - 17.91}{11.86}=\frac{10.29}{11.86}\approx0.87$

Step2: Determine if it's unusual

In a normal distribution, values are considered unusual if they are more than 2 standard deviations from the mean (i.e., $|z|> 2$). Since $|0.87|<2$, the value is not unusual.

Answer:

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