Question

Q 1) The height measurements of 600 adult males are arranged in ascending order and it is observed that 180th and 450th entries are 46.3 and 67.8 inch respectively. If the measurements are normally distributed.

i. Find the mean and the standard deviation of the distribution.

ii. Find the number of males whose height is between 40 and 70 inches.

Q 2) In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and standard deviation of 200. what is the lowest possible score a student needs to qualify for acceptance into the university.

Q 3) Ahmed plays a game where he tosses two balanced 4 sided-dice, each with faces labeled by 1, 2, 3 and 4. He wins 2 points if the sum is 4. He wins 1 point if the sum is greater than 4. He loses k points if the sum is less than 4.

i. Find the probability distribution sum.

ii. Find the value of k which achieves the fairness of game. (i.e. The fairness is achieved if the game is not biased neither to loss or win)

Q 4) Given that the expected number of defective machines is 2 if 20 machines are shipped.

i. Find the probability of good machines manufactured by the company.

ii. What is the probability that at least 4 are defective?

iii. What are the expected number and standard deviation of good machines in a sample of 50?

Answer 1