A salesman makes 50 calls during a particular week. You may assume that independently for each house visited, the probability of a sale is 0.2.

a] Find the probability that during this week, he makes

i) exactly 12 sales,

ii) between 10 and 14 (both inclusive) sales,

iii) his first sale on the third house visited. [9]

b] At the end of the week, he is paid £100 plus a commission of £50 for every sale. Find the mean and standard deviation of his total pay for this week. [5]

For a]i), I used the binomial formula and got 0.1033 (to 4dp)

For ii) I did P(X $\displaystyle \leq$ 10) - P(X $\displaystyle \leq$ 15) and taking these from my table values, I got 0.4956.

For iii) I got confused - but I think it would be done byfailurexfailurexsuccesswhich is 0.8 x 0.8 x 0.2 which is 0.128. Can't say I'm too confident about this.

But what about part b? I've never known a question like this and hope it doesn't come up in the exam. How would you answer this?

Thanks if you can help