Attempt all the problems.
problem1) Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class as follows:
Quiz 1 60 60 60 60 71 73 74 75 88 99
Quiz 2 65 65 65 65 70 74 79 79 79 79
Quiz 3 66 67 70 71 72 72 74 74 95 99
Quiz 4 10 49 70 80 85 88 90 93 97 98
a) find out the mean, median, mode for each quiz.
b) Based on the results obtained in (a) above, indicate measure of central tendency you will like to use for each of the quizzes with reasons.
problem2) A biometric security devise using fingerprints erroneously refuses to admit 1 in 1000 authorized persons from the facility containing classified information. The device will erroneously admit 1 in 10,00,000 unauthorized persons. Suppose that 95% of those who seek access are authorized. If the alarm goes off and a person is refused admission, what is the probability which really authorized?
problem3) Assume waiting time to get food after placing the order at the fast-food restaurant is exponentially distributed with the mean of 60 seconds. If a randomly selected customer orders food at the restaurant, what is the probability that the customer would have to wait at least two minutes?
problem4) A family has two children – one male child and the other female child. Both the children are grown up and their daily expenditure is believed to be normally distributed with the mean of Rs.80 and Rs.60 for the male and the female child with standard deviation of Rs.20 and Rs.10 respectively. Determine the probability that two children together have an expenditure of more than Rs. 160.
Car manufacturer who is producing cars at a rate of 4000 cars a month needs to procure ignition equipment from vendors. Company has the policy of placing orders for 12000 ignition equipment every time they order. The vendor has indicated that 3 % of the ignition equipment is likely to be faulty in each shipment. As it is not possible to test each and every ignition equipment by the car manufacturer, manufacturer decides to randomly sample 200 ignition equipment and if more than 2 of them are found to be defective the entire batch of order shall be returned back.
a) What sampling method will you suggest for car manufacturer?
b) What is the probability that the batch would be returned back to the vendor.