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.

0.0076, if you meant 4.125 divided by 0.03125 it would be 132

step-by-step explanation:

first you have to move the decimal in 0.03125 over until its behind the 5 which is 5 places over. now the number is 3125

then you have to move the decimal in 4.125, 5 places over. now the number is 4,112,500.

now you divide like you would normally would and get 0.0076