# Statistics

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4. A coil of wire has 600 metres of wire. Suppose there are 20 nicks (the most common problem with wire) are randomly distributed on a coil.
a) What is the probability that in a 60 metre length of wire there will be at least 3 nicks?
b) What is the probability that in a 47 metre length of wire there will be exactly 4 nick(s)?

5. Two students have started a business to seal driveways during the summer months. They rent a pickup truck and a power sprayer. With this they will use a tar based spray to seal asphalt driveways. Past experience has shown that the best time to sign up customers is to ring their doorbells between 5:00 and 8:00 p.m. on any weekday evening. Any jobs that they obtain will be completed the next day. In the months of June. July and August they find that they get an average of 2.5 customers per hour ringing doorbells.
a) What is the probability that they will get from 4 to 10 jobs in an evening of soliciting?
b) They charge \$25 per driveway. If the truck costs \$65 per day, and the spraying equipment costs \$20 per day and the material to seal one driveway costs \$6, what is the probability that they will make a profit on any given day.

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