Mathematics, 28.05.2021 14:00 hiyagirllyric

Assume that females have pulse rates that are normally distributed with a mean of beats per minute and a standard deviation of beats per minute. a. If 1 adult female is randomly selected, find the probability that her pulse rate is between beats per minute and beats per minute.
b. If 4 adult females are selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 76 beats per minute.
c. Why can the normal distribution be used in heartbeat even the sample side does not exceed 30?

Answers: 2

Show answers

Answers

Answer from: timiaparker

a) This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.

b) P-value of Z when X = 76 subtracted by the p-value of X = 68.

c) Because the underlying distribution(pulse rates of females) is normal.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Mean $\mu$ , standard deviation $\sigma$ .

standard deviation of beats per minute.

a. If 1 adult female is randomly selected, find the probability that her pulse rate is between A beats per minute and B beats per minute.

This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.

b. If 4 adult females are selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 76 beats per minute.

Sample of 4 means that we have $n = 4, s = \frac{\sigma}{\sqrt{4}} = 0.5\sigma$

The formula for the z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{X - \mu}{0.5\sigma}$

$Z = 2\frac{X - \mu}{\sigma}$

This probability is the p-value of Z when X = 76 subtracted by the p-value of X = 68.

c. Why can the normal distribution be used in heartbeat even the sample side does not exceed 30?

Because the underlying distribution(pulse rates of females) is normal.

Answer from: Quest

you never say the total so we cant find the percentage used for petrol

step-by-step explanation:

Answer from: Quest

When i did the math i got 11 cm
Each rectangle in the figure below is congruent and measures 2 cm x 1/2 cm what is the term perimete

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Which fraction is not equivalent to 8/12 a. 2/3 b. 24/36 c. 4/10 d. 6/10

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)+0

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

Aladder that is 20ft long is leaning against the side of a building. if the angle formed between the ladder and the ground is 75 degrees how far is the bottom of the from the base of the building?

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.

Answers: 2

Answer

You know the right answer?

Assume that females have pulse rates that are normally distributed with a mean of beats per minute a...

Questions