Question

1. Jade is renovating his bathroom and as part of the renovations a plumber is required to install a new shower. The budget for this part of the renovations is $1000. An industry expert has told Jade that the probability that a randomly selected plumber in Auckland will be able to do the job for $1000 or less is 0.55, and that a list of plumbers located in Auckland is available from the Plumbers, Gasfitters and Drainlayers Board website. There are a very large number of plumbers in Auckland.

(a) Suppose that Jade randomly selects 10 plumbers from the list of Auckland plumbers. What is the probability that exactly 2 plumbers will be able to install the new shower for $1000 or less?Answer this question using the appropriate mathematical formula.

(b) What is the probability that Jade will have to call at least 4 plumbers to find one that can do the job for $1000 or less?
Answer this question using the appropriate mathematical formula.

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

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

(e) Suppose that Jade wants to select a plumber close to where he lives. Within his suburb there are 10 plumbers available and of these, 6 would do the job for $1000 or less. What is the probability that Jade will have to call exactly 4 plumbers before finding one who will do the job for $1000 or less? (i.e. the 4th plumber called will do the job).

Answer 1