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Statistics and probability

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Hello. Can anybody help e with these 6 example questions that were created. I want to use them as a study guide.

1. An unprepared student makes random guesses for the 10 true-false questions on a pop quiz. Find the probability that there is at least once correct answer.

2. A box contains four red, three blue, and six green marbles. Two marble are randomly selected from the box. Find the probability of getting two red marbles when two are selected if the first is not replaced before the second selection is made.

3. A supplier must fill four large orders. How many different ways can those orders be organized?

4. How many different three person study groups can be formed from a class of nineteen students?

5. Which is better and corresponds to the higher relative position, a score of 92 on a test with mean of 71 and standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

6. For the given sample data 62, 52, 52, 52, 64, 69, 69, 76, find

A. Standard deviation:
B. P
C. Percentile rank of a score of 64

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https://brainmass.com/math/probability/statistics-and-probability-256273

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This provides examples of finding standard deviation, probability, and counting techniques.

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Statistics and Probability in Computing

1) When sending data over the internet there is a certain probability that a message will be corrupted. One way to improve the reliability of getting messages through is to use a Hamming Code. This involves sending extra data that can be used to check the main message. For example a 7 bit Hamming Code contains 4 bits of message data and 3 check bits. If only one of the bits is in error at the receiving end then mathematical techniques can be used to determine which one it is and apply a correction. Assume that you have a network connection for which the probability that an individual bit will get through without error is 0.66. What is the increase in the probability that a 4 bit message will get through if a 7 bit Hamming code is used instead of just sending the 4 bits? (i.e what is P(7 bits with 0 or 1 error) - P(4 bits with no error)?

2) Q Computers has invented quantum computers. Each computer contains an exotic sub-atomic particle. Unfortunately this particle decays in the same manner as all radioactive particles. Therefore an average quantum computer only lasts for 22 months. The University has purchased one of these computers and Professor Squiggle wants to use it for 7 months. When he tries to book it he finds that it is already booked out for the first 8 months. So he books it for the next 7 months. What is the probability that the computer will fail during the time that professor Squiggle is using it (not before and not after)?

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