Assume that females have pulse rates that are normally distributed with a mean of u = 74.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 77 beats per minute. The probability is. (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 77 beats per minute. The probability isO: (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? O A. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size. O B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. O C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. O D. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

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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.