5. A manufacturer of digital recorders claims the distribution of life of its recorders can be described by a normal distribution with a mean of 2500 hours and variance of 40000 hours. (15%) a. What is the probability that a randomly selected digital recorder lasts more than 2250 hours? b. If two digital recorders are randomly selected, what is the probability of neither lasting more than 2250 hours? c. If my digital recorder lasted longer than 28% of all the digital recorders, exactly how many hours was the life of my digital recorder? d. What is the sampling distribution of the sample mean of 64 random observations from this population? Find the probability of sample mean being between 2490 and 2518. c. Would your results in parts a - d remain valid if the life of digital recorders did not have a normal distribution? Explain.

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Q: If det (AB²) = 24 and det(AB) = 8, what is det (BT) equal to?

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Q: The only solution to arcsin is - π 4 True O False (- √√2 2

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.