Question

Let be the density function for the shelf life of a brand of banana which lasts up to weeks. Time, , is measured in weeks and . Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place. Mean

Answer 1

The question is incomplete. The complete question is :

Let
`p(t) = -0.0375t^2 + 0.225t` be the density function for the shelf life of a brand of banana which lasts up to 4 weeks. Time, t, is measured in weeks and
`$0 \leq t \leq 4$`. Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place.

Answer:

2.4

Explanation:

Given :

`p(t) = -0.0375t^2 + 0.225t`

Mean :

`$=\int_0^4 tp (t) \ dt$`

`$=\int_0^4 t (0.0375 t^2 + 0.225t) \ dt$`

`$=-0.0375 \int_0^4 t^3 \ dt + 0.225 \int_0^4 t^2 \ dt$`

`$=-0.0375 \left[ (t^4)/(4) \right]^4_0 + 0.225 \left[ (t^3)/(3) \right]^4_0$`

`$=-0.0375 (64) + 0.225 \left( (64)/(3) \right)$`

`$=-2.5 + 4.8$`

= 2.4

Therefore, the mean is 2.4