Question

the times for the passage of play in a rugby game have a mean of 19.25 seconds with a standard deviation of 12 seconds. suppose a passage of play in a rugby game takes 2.7 seconds. would it be unusual for this to happen?

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

Explanation:

Step1: Calculate z-score

$z = \frac{x - \mu}{\sigma} = \frac{2.7 - 19.25}{12} \approx -1.38$

Step2: Compare absolute z-score to 2

$|z| \approx 1.38 < 2$, so within 2 SD.

Step3: Determine unusualness

Values within 2 SD are not unusual.

Answer:

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