S2 Revision Quiz Answers coming up…
Question 1 (3 points)
A string AB of length 5 cm is cut, in a random place C, into two pieces. The random variable X is the length of AC.
Write down the name of the probability distribution of X and sketch the graph of its probability density function
Question 5 (1 mark)
An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour.
Suggest a suitable model for the number of faulty parts per hour
Question 6 (2 marks)
An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour.
Describe two assumptions that are necessary to model the number of faulty parts using a Poisson Distribution.
Question 7 (2 marks)
An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour.
Find the probability of 2 faulty parts being detected in a 1 hour period.
Question 8 (3 marks)
An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour.
Find the probability of at least one faulty part being detected in a 3 hour period.
Question 9 (3 marks)
A bag contains a large number of coins:
75% are 10p coins
25% are 5p coins
Write down all the possible combinations of 3 coins that you could select from the bag
Question 10 (1 mark)
A bag contains a large number of coins:75% are 10p coins25% are 5p coins
Write down the possible medians of all the samples of 3 coins that you could select from the bag
Question 11 (3 marks)
A bag contains a large number of coins:75% are 10p coins25% are 5p coins
A random sample of 3 coins is selected.Find the sampling distribution for the median of the values of the 3 selected coins.
Question 12 (2 marks)
Write down the 2 conditions under which the Poisson distribution may be used as an approximation to the Binomial distribution.
Question 13 (2 marks)
A call centre routes telephone calls. The probability of a call being wrongly connected is 0.01
Find the probability that 2 consecutive calls will be wrongly connected.
Question 14 (3 marks)
A call centre routes telephone calls. The probability of a call being wrongly connected is 0.01
Find the probability that more than 1 in 5 consecutive calls will be wrongly connected.
Question 15 (3 marks)
A call centre routes telephone calls. The probability of a call being wrongly connected is 0.01The call centre receives 1000 calls each day. Find the mean and variance of the number of incorrectly connected calls.
Question 16 (2 marks)
A call centre routes telephone calls. The probability of a call being wrongly connected is 0.01. The call centre receives 1000 calls each day.
Use a Poisson approximation to find the probability that more than 6 calls each day are wrongly connected. Give your answer to 3 dp.
Question 17 (2 marks)
Write down 2 conditions for a Normal distribution to be used to approximate a Binomial distribution.
Question 18 (2 marks)
A Normal distribution is to be used to approximate a Binomial distribution.
Write down the mean and variance of this normal approximation in terms of n and p.
Question 19 (5 marks)
A factory makes 2000 DVDs each day.
3% of all DVDS made are faulty.
Use a normal approximation to estimate the probability that at least 40 faulty DVDs are produced in a day.
Question 20 (3 marks)
A factory makes 2000 DVDs each day. 3% are faulty
It costs £0.70 to make each DVD. Non-faulty DVDs are sold for £11 each. Faulty DVDs are destroyed
Find the expected profit made by the factory per day.