Question

Bailey is an inquisitive kitten that likes to play a game with his humans called "No take, only throw". After his humans throw his toy, he'll fetch his toy but won't take it back to them. The amount of time Bailey will play with his toy before he meows at his humans to come get his toy for more throwing follows a uniform distribution from 28.4 to 50 seconds. What is the 30th percentile of the amount of time Bailey will play with his toy before meowing at his humans to throw it again? (Round your final answer to 2 decimal places)

Answer 1

To find the 30th percentile of the amount of time Bailey will play with his toy before meowing, we can use the formula for a uniform distribution:

Percentile = Minimum + (Percentile Rank / 100) (Maximum - Minimum)

In this case:

Minimum = 28.4 seconds

Maximum = 50 seconds

Percentile Rank = 30

Plug these values into the formula:

Percentile = 28.4 + (30 / 100) * (50 - 28.4)

Percentile = 28.4 + (0.30) * (21.6)

Now, calculate:

Percentile = 28.4 + 6.48

Percentile ≈ 34.88 seconds

So, the 30th percentile of the amount of time Bailey will play with his toy before meowing at his humans to throw it again is approximately 34.88 seconds (rounded to 2 decimal places).