(c) Daily costs (in dollars) are given byㄒ

$$C = 100 + 0.95X$$

where X is the number of hamburgers sold. Find the mean and standard deviation of daily profits from sales.

(15%)3. A consultant knows that it will cost her $10,000 to fulfil a particular contract. The contract is to be put out for bids, and she believes that the lowest bid, excluding her own, can be represented by a distribution that is uniform between $8,000 and $20,000. Therefore, if the random variable X denotes the lowest of all other bids (in thousands of dollars), its probability density function is

$$f_x(x) = \begin{cases} \frac{1}{12}, & \text{for } 8 < x < 20 \\ 0, & \text{for all other values of } x \end{cases}$$

(a) What is the probability that the lowest of the other bids will be less than the consultant's cost estimate of $10,000?