Assume that females have pulse rates that are normally distributed with a mean of
mu equals μ=74.0 beats per minute and a standard deviation of
sigma equals σ=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.
b. if 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 80 beats per minute.
c. why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Step-by-step explanation:

a. First, find the z-score.

z = (x − μ) / σ

z = (80 − 74.0) / 12.5

z = 0.48

Use a calculator or table to find the probability.

P(z < 0.48) = 0.6844

b. Find the standard deviation of the sample.

σₓ = σ / √n

σₓ = 12.5 / √4

σₓ = 6.25

Find the z-score.

z = (x − μ) / σ

z = (80 − 74.0) / 6.25

z = 0.96

Use a calculator or table to find the probability.

P(z < 0.96) = 0.8315

c. When the distribution of the population is normal, then the distribution of the sample mean is also normal.

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right