Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard deviation of sigma equals 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 80 beats per minute. The probability is nothing. (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 80 beats per minute. The probability is nothing. (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? A. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. D. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Let x be a random variable representing pulse rate of adult females. Since the pulse rates are normally distributed, then according to the central limit theorem,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 74

σ = 12.5

a) P(x < 80)

For x = 80,

z = (80 - 74)/12.5 = 0.48

Looking at the normal distribution table, the probability corresponding to the z score is 0.6844

P(x < 80) = 0.6844

b) Since the number of samples, n = 25, then the formula would be

z = (x - µ)/(σ/√n)

z = (80 - 74)/(12.5/√25) = 2.4

Looking at the normal distribution table, the probability corresponding to the z score is 0.9918

P(x < 80) = 0.9918

c) the normal distribution can be used in part b because

C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

where is the figure