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The number of content changes to a Web site follows a Poisson distribution with a mean of
0.25 per day.
a. What is the probability of two or more changes in a day?
b. What is the probability of no content changes in five days?
c. What is the probability of two or fewer changes in five days?
If a publisher of nontechnical books takes great pains to ensure that its books are free of
typographical errors, so that the probability of any given page containing at least one such error is 0.005
and errors are independent from page to page,
a. What is the probability that one of its 400-page novels will contain exactly one page with errors?
b. What is the probability that one of its 400-page novels will contain exactly one page with errors
given that it contains at least one page with errors?
A parabolic satellite dish reflects signals to the dishβs focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function ππ₯(π₯) = { π (1 β 1 /16* π₯*2) , 0 < π₯ < 2; 0, ππ‘βπππ€ππ π where X is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. Determine the following: a. Value of π that makes ππ₯(π₯) a valid probability density function. b. π(0.1 < π < 0.4). c. πΈ(π) and πππ(π)
Suppose that 2 batteries are randomly chosen without replacement from the following groupof 9 batteries: 3 new, 4 used (working), 2 defective. Let X denote the number of new batteries chosen. Let Y denote the number of used batteries chosen. a. Find the joint probability distribution, π(π = π₯, π = π¦). b. Find πΈ[π].
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?Β
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?Β
Β 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 Ξ» = 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 doesnβt 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 possibleΒ for Carlos to raise his score to an 18?
A square matrix is nonsingular if it can be written as a product of elementary matrices.
#339914 on Dec 2023