Reference no: EM131106923

An ethologist is interested in how long it takes a certain species of water shrew to catch its prey. On 20 occasions each day he lets a dragonfly loose inside the cage of the shrew and times how long it takes until the shrew catches the dragonfly. After months of research the ethologist concludes 1) that the mean prey catching time was 30 seconds, 2) the standard deviation was 5.5 seconds and 3) that the scores he has collected are normally distributed. (Note: remember that the proportions in the Z-table can also be viewed as probabilities.) Based on the shrew's past record, what is the probability:

1. It will catch a dragonfly in less than 18 seconds;

2. It will catch a dragonfly in between 22 and 45 seconds;

3. It will take longer than 45 seconds to catch a dragonfly?

4. Explain your method in calculating these probabilities. (Note: remember that the proportions in the Z-table can also be considered as representing probabilities.)