A baker put 500 raisins into dough, mixed well, and made 100 cookies. You take a
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A baker put 500 raisins into dough, mixed well, and made 100 cookies. You take a random cookie. What is the probability of finding at least 4 raisins in it? In the last four months, I had to replace five light bulbs in my house. What are the chances that I won't need to change a lightbulb next month? It is estimated that one in ten parked cars do not pay the parking fare. A parking inspector is inspecting 20 cars and will give out fines to those who did not pay for parking. (a) What are the chances that the inspector does not give out any fines? (b) What are the chances that exactly 2 cars will get a fine? (c) What are the chances that at least 2 cars will get a fine? (d) It costs $1 to inspect each car, and each parking fine is for $20. The inspection company will make money if it collects more fines than it spends on inspecting the cars. What is the minimum number of cars that the company should inspect to be at least 95% sure that it will make money? A radioactive source emits 4 particles on average during a five-second period. (a) Calculate the probability that exactly 4 particles are emitted during a 5-second period. (b) Calculate the probability that at least 4 particles are emitted during a 5-second period. Air Canada estimates that 1% of its customers with purchased tickets fail to show up for their flights. For one particular flight, the plane has 300 seats and the flight has been fully booked. How many additional tickets can the airline sell so that there is at least a 90% chance that everyone who shows up will have a seat?Explanation / Answer
It seems the Q.N. 10 is incomplete. Please find the sample answer for Q. No. 5 only as mistakenly I have accepted the questions where Q.No.10 is not complete.
Sol. 5) In this case we will use Poisson approximation to Binomial distribution to find out the number raisins in one Cookie
The number of raisins X in one cookie is Binomial with n = 500 and p = 0.01.
Which is approximately Poisson with parameter np = 500*0.01 = 5
The probability of finding at least 4 raisins will be given by P(X 4) = 1 F(3) = 1 0.265 = 0.735
(From the Poisson Table - please refer the poisson table to see the value)
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