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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.
Carl has completed 8 math homework assignments that are all worth 20 points, and his mean score is 17. Carlos has two more 20-point homework assignments to complete before his progress report gets sent out, and he wanted to raise his mean score to an 18. Is it possible for Carlos to raise his score to an 18?
A tennis ball of mass 0.0551kg is served. It strikes the ground with a velocity of 54.0m/s at an angel of 22° below the horizontal. Just after the bounce it is moving at 53.0m/s at an angel of 18° above the horizontal. If the interaction with the ground lasts 0.0610 s, what is the magnitude of the average force exerted by the ground on the ball?
Find canonical form of Zxx +Zyy=y
If the pH of a substance is 4, what will the pOH be?
A bulb manufacturer claims that the lives of its bulbs are normally distributed with a mean of 6000 hours and a standard deviation of 400 hours. A random sample of 16 bulbs had an average life of 5850 hours. If the manufacturer’s claim is correct-
a. What is the sampling distribution of the sample mean?
b. what is the probability of finding a sample mean of 5850 or less?
An archer shoots an arrow towards a 300g target that is sliding in her direction at a speed of 2.50m/s on a smooth frictionless surface. The 22.5g arrow is shot with speed of 35m/s and passes through the target without changing the mass of the target, which is stopped by the impact. Calculate the speed of the arrow after passing through the target?
#340153 on Dec 2023