Math Answers

Toss a fair coin twice. You win Ghc 1 if at least one of the two tosses comes out heads.

(a) Assume that you play this game 300 times. What is, approximately, the probability that you win at least Ghc 250?

(b) Approximately how many times do you need to play so that you win at least Ghc 250 with probability at least 0.99?

 How many times do you need to toss a fair coin to get 100 heads with probability 90%?

 Suppose it is known that the weight of a certain population of individuals are approximately normally distributed with a mean 80 kg and a standard deviation of 16 kg. What is the probability that a person picked at random from this group will weight between 60 and 110 kg?

 Suppose that all athletes run 200 metres and the time they take to run is normally distributed with mean 12 seconds and a standard deviation of 3 seconds. The coach has decided that 40 percent of the athletes who can run the distance in the least time will be sent to participate in the Olympics. What is the cutoff score that will be decide which members of the time will qualify.

Solve 𝑧𝑝 = −𝑥.

 The length of time patients must wait to see a doctor at an emergency room of a large hospital is uniformly distributed between 40 minutes and 3 hours. What is the probability that a patient will have to wait between 50 minutes and 1.5 hours to see a doctor?

According to the Insurance Institute of America, a family of four spends between Ghc 400 and Ghc 3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.

(a) What is the mean amount spent on insurance?

(b) What is the standard deviation of the amount spent?

(c) If we select a family at random, what is the probability they spend less than Ghc 2,000 per year on insurance per year?

(d) If we select a family at random, what is the probability they spend less than Ghc 2,000 per year on insurance per year? (e) What is the probability a family spends more than Ghc 3,000 per year?

The number of people arriving for treatment at an emergency room can be modelled by a Poisson process with a mean of five people per hour.

(a) What is the probability that exactly four arrivals occur at a particular hour?

(b) What is the probability that at least four people arrive during a particular hour?

(c) How many people do you expect to arrive during a 45-min period?

An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil.

(a) What is the probability that the first strike comes on the third well drilled?

(b) What is the probability that the third strike comes on the seventh well drilled?

(c) What is the mean and variance of the number of wells that must be drilled if the oil company wants to set up three producing wells?

A pipe-smoking mathematician always carries two boxes of matches - one is his right pocket and another in his left pocket. Each time he needs a match, he is equally likely to take it from either pocket. Suppose that each box initially contains n matches. What is the probability that once the mathematician discovers that one of the boxes is empty, there are exactly k matches in the other box, k = 0,1,...n?