TUTORIAL 4 1. Solve these: a. If X ~ Bin (9, 0.2), find P(X = 5). b. If X ~ Bin (9, 0.5), find P(X = 5). 2. 1% of a large consignment of ballpoint pens is known to be defective. A random sample of 20 pens is taken from the consignment and X is the random variable denoting the number of defective pens in the sample, find a. n and p where X ~ Bin (n,p). b. P(X = r) for r = 0, 1 and 2. c. P(X > 2). 3. In a large population, 16% of the people are left-handed. In a random sample of 10 find a. b. c. d.
The probability that exactly 2 will be left-handed. The probability that fewer than 2 will be left-handed. The probability that more than 2 will be left-handed. The probability that between 2 and 6 will be left-handed.
4. Kuala Terengganu Hospital keeps records of emergency room traffic. Those records reveal that the number of patients who arrive between 6:00 P.M. and 7:00 P.M. has a Poisson distribution with parameter λ = 6.9. Determine the probability that, on a given day, the number of patients who arrive at the emergency room between 6:00 P.M. and 7:00 P.M. will be a. b. c. d. e. f.
Exactly four. At most two. At least three. Between four and 10, inclusive. Determine and interpret the mean of the random variable X. Determine the standard deviation of X.
5. A workshop tows in an average of five damaged cars per week. Assuming that the number of damaged cars towed per week has a Poisson distribution, find the probability that a. b. c. d.
Exactly 5 cars are towed in a particular week. At least 5 cars are towed in a particular week. Exactly 20 cars are towed in a four-week period. For four successive weeks, at least 5 cars are towed in each week.
6. A proof reader discovers 200 misprints in a book containing 800 pages. Assuming that the misprints occur at random, find the probability that a particular page contains a. No misprint. b. One or two misprints. c. More than two misprints
7. Particles are emitted randomly from a radioactive substance at an average of 4 particles every 5 seconds. a. Find the probability that exactly two particles are emitted in a second period. b. Find the probability that no emission occurs in 15 seconds. c. The probability that at least one emission occurs in the next t seconds is 0.9. Find the value of t. 8. The second leading genetic cause of mental retardation is X Syndrome, named for the fragile. One in 1500 males are affected world-wide, with no ethnic bias. a. In a sample of 10,000 males, how many would you expect to have X Syndrome? b. For a sample of 10,000 males, use the Poisson approximation to the binomial distribution to determine the probability that more than 7 of the males have X Syndrome; that at most 10 of the males have Fragile X Syndrome.
DUE DATE: 20/03/2017 before 12.00 P.M The answer for the tutorial must be sent to the following email:
[email protected]
