Chapter 9, Problem 60RE

(a)

To determine

To calculate: The mean and standard deviation of the random variable x which is the daily demand (in hundreds of pounds) for a certain product with the probability density function $f\left(x\right)=\frac{6}{125}x\left(5-x\right)$ over the interval $\left[0,5\right]$.

(b)

To determine

To calculate: The median of the random variable x which is the daily demand (in hundreds of pounds) for a certain product with the probability density $f\left(x\right)=\frac{6}{125}x\left(5-x\right)$ over the interval $\left[0,5\right]$.

(c)

To determine

To calculate: The probability that the demand is within one standard deviation of the mean of the daily demand (in hundreds of pounds) for a certain product with the probability density function $f\left(x\right)=\frac{6}{125}x\left(5-x\right)$ over the interval $\left[0,5\right]$.