1. A radar unit is used to measure the speed of automobiles on the expressway during the rush-hour traffic. The observer measures 76 cars and obtains the mean speed of 62.0 mph. For reference, compare this problem with Problem 1 of EX 07. (a) Assuming the standard deviation is about 4.95 mph, find the 95% confidence interval of the mean speed of the cars. (b) Find the 95% upper confidence bound, using the standard deviation of Part (a). (c) If the 90% upper confidence bound is 63.5 mph, what is the standard deviation? (d) Find the 98% confidence interval, using the standard deviation of Part (c). (e) Find the 99% lower confidence bound, using the standard deviation of Part (c).

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A: mode is most frequency value

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Q: Please answer the subparts d and e. thank you!

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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.