Statistics and Probability Answers

A stamping machine produces ‘can tops’ whose diameters are normally distributed with a standard deviation of 0.02 inch. At what nominal mean diameter should the machine be set, so that no more than 9 % of the ‘can tops’ produced have diameters exceeding 3.5 inches?

A stamping machine produces ‘can tops’ whose diameters are normally distributed with a standard deviation of 0.02 inch. At what nominal mean diameter should the machine be set, so that no more than 9 % of the ‘can tops’ produced have diameters exceeding 3.5 inches?

A stamping machine produces ‘can tops’ whose diameters are normally distributed with a standard deviation of 0.02 inch. At what nominal mean diameter should the machine be set, so that no more than 9 % of the ‘can tops’ produced have diameters exceeding 3.5 inches?

One bag contains 4 white balls and 3 black balls and a second bag contains 3 white balls and 5 black balls. One ball is drawn from the first bag and placed unseen in second bag. What is the probability that a ball now drawn from the second bag is black?

(a) The probability that a man aged 60 will live to be 70 is 0.65. What is the probability that out of 10 men, now aged60 (i) exactly 9 will live to be 70 (ii) at most 9 will live to be 70, and (iii) at least 7 will live to be 70?

(b) In an examination taken by 500 candidates, the average and S.D of marks obtained are 40% and 10% respectively. Assuming normal distribution, find (i) how many have scored above 60%,(ii) how many will pass if 50% is fixed as the minimum marks for passing, (iii) how many will pass if 40% is fixed as the minimum marks for passing, and (iv) what should be the minimum percentage of marks for passing so that 350 candidates pass.

(a) One half percent of the population has a particular disease. A test is developed for the disease. The test gives a false positive 3% of the time and a false negative 2% of the time. (a). What is the probability that Joe (a random person) tests positive? (b). Joe just got the bad news that the test came back positive; what is the probability that Joe has the disease?

(b) Three cooks, A, B and C bake a special kind of cake, and with respective probabilities 0.02, 0.03, and 0.05 it fails to rise. In the restaurant where they work, A bake 50 percent of these cakes, B 30 percent and C 20 percent. What proportion of failures is caused by A

(a) A stamping machine produces ‘can tops’ whose diameters are normally distributed with a standard deviation of 0.02 inch. At what nominal mean diameter should the machine be set, so that no more than 9 % of the ‘can tops’ produced have diameters exceeding 3.5 inches?

(b) Let A and B be independent events with P (A) = 1/4 and P (A U B) = 2P (B) − P (A).
Find (a). P (B); (b).P (A|B); and (c). P (Bc|A).

1. (a) A player tosses 3 fair coins. He wins Rs.500 if 3 heads appear, Rs.300 if 2 heads appear, Rs.100 if 1 head occurs. On the other hand, he loses Rs.1500 if 3 tails occur. Find the expected gain of the player and variance.

In a test on electric bulbs, it was found that the life time of a particular brand was normally distributed with an average life of 2000 hours and S.D. of 60 hours. If a firm purchases 2500 bulbs, find the number of bulbs that are likely to last for (i) more than 2100 hours, (ii) less than 1950 hours and (iii) between 1900 and 2100 hours.

A class contains 10 boys and 20 girls of which half the boys and half girls have brown eyes. Find the probability that a student chosen at random is a boy or has brown eyes.