Math Answers

DETERMINE THE NUMBER OF SETS OF ALL POSSIBLE RANDOM SAMPLES THAT CAN BE DRAWN FROM THE GIVEN POPULATION BY USING THE FORMULA, NCn.

N = 10, n = 3

IDENTIFY WHICH SAMPLING METHOD IS APPLIED. A SAMPLE OF 15 MICE ARE SELECTED AT RANDOM FROM A SET OF 50 MICE TO TEST THE EFFECT OF A CERTAIN MEDICINE.

DETERMINE THE NUMBER OF SETS OF ALL POSSIBLE RANDOM SAMPLES THAT CAN BE DRAWN FROM THE GIVEN POPULATION BY USING THE FORMULA, _NC_n.N = 5, n = 3.

Determine the dimensions of the right circular cylinder of

greatest volume that can be inscribed in a right circular cone of

radius 6 cm and height 9 cm.

A company that produces batteries claims that the life expectancy of their batteries is 90 hours with a standard deviation of 10 hours. A consumer interest group believes that the actual battery life expectancy of these batteries is shorter than the claimed battery life. In order to prove this, they test a random sample of 20 batteries which resulted a mean of 87 hours. Conduct a hypothesis test with a significance level of 0.05

A company that produces batteries claims that the life expectancy of their batteries is 90 hours with a standard deviation of 10 hours. A consumer interest group believes that the actual battery life expectancy of these batteries is shorter than the claimed battery life. In order to prove this, they test a random sample of 20 batteries which resulted a mean of 87 hours. Conduct a hypothesis test with a significance level of 0.05

For each day, independent of the others, the length of time for one individual to be servedat a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. What is the probability that a person is served in less than 3 minutes on at least 4 of the next 6 days?

A credit card company monitors cardholder transaction habits to detect any unusual activity. Suppose that the dollar value of unusual activity for a customer in a month follows a normal distribution with mean $250 and variance $391. a. What is the probability of $250 to $300 in unusual activity in a month? b. What is the probability of more than $300 in unusual activity in a month? c. Suppose that 10 customer accounts independently follow the same normal distribution. What is the probability that at least one of these customers exceeds $300 in unusual activity in a month? 

The life of a certain type of automobile tire is normally distributed with mean 34,000 miles and standard deviation 4000 miles. a. What is the probability that such a tire lasts over 40,000 miles? b. What is the probability that it lasts between 30,000 and 35,000 miles? c. Given that it has survived 30,000 miles, what is the conditional probability that it survives another 10,000 miles? 

 A hospital keeps records of its emergency-room traffic. Those records indicate that, beginning at 6:00 P.M. on any given day, the elapsed time until the first patient arrives has an exponential distribution with parameter λ = 6.9, where time is measured in hours. Determine the probability that, beginning at 6:00 P.M. on any given day, the first patient arrives

a. between 6:15 P.M. and 6:30 P.M.

b. before 7:00 P.M.

c. given that the first patient doesn’t arrive by 6:15 P.M., determine the probability that she arrives by 6:45 P.M.