1. Jade is renovating his bathroom and as part of therenovations a plumber is required to install a new shower. Thebudget for this part of the renovations is $1000. An industryexpert has told Jade that the probability that a randomly selectedplumber in Auckland will be able to do the job for $1000 or less is0.55, and that a list of plumbers located in Auckland is availablefrom the Plumbers, Gasfitters and Drainlayers Board website. Thereare a very large number of plumbers in Auckland.

(a) Suppose that Jade randomly selects 10 plumbers from the listof Auckland plumbers. What is the probability that exactly 2plumbers will be able to install the new shower for $1000 orless?Answer this question using the appropriate mathematicalformula.

(b) What is the probability that Jade will have to call at least4 plumbers to find one that can do the job for $1000 or less?
Answer this question using the appropriate mathematicalformula.

(c) What is the expected number of calls that Jade will have tomake to find a plumber who can do the job for $1000 or less? Whatis the variance of the number of calls?

(d) Of the plumbers that will install the shower for $1000 orless, the cost of the job (in dollars) has a uniform distributionon the interval (450,1000). What is the expected value and variancefor the cost of installing the shower?

(e) Suppose that Jade wants to select a plumber close to wherehe lives. Within his suburb there are 10 plumbers available and ofthese, 6 would do the job for $1000 or less. What is theprobability that Jade will have to call exactly 4 plumbers beforefinding one who will do the job for $1000 or less? (i.e. the 4thplumber called will do the job).