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

Step-by-step explanation:

 Given :

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

Mean :

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

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

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

$=-0.0375 \left[ \frac{t^4}{4} \right]^4_0 + 0.225 \left[ \frac{t^3}{3} \right]^4_0$

$=-0.0375 (64) + 0.225 \left( \frac{64}{3} \right)$

$=-2.5 + 4.8$

= 2.4

Therefore, the mean is 2.4