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

auto insurance

step-by-step explanation:

Answer from: Quest

The answer mai bc

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Determine the quotient and remainder when (6a3)+11a2-4a-9) is divided by (3a-2) express your answer in the form q(a) + r(a)/d(a)

Answers: 1

Answer

Mathematics, 21.06.2019 16:50

Which is a true statement comparing the graphs of x^2/6^2-y^2/8^2 = 1 and x^2/8^2-y^2/6^2 the foci of both graphs are the same points. the lengths of both transverse axes are the same. the directrices of = 1 are horizontal while the directrices of = 1 are vertical. the vertices of = 1 are on the y-axis while the vertices of = 1 are on the x-axis.

Answers: 2

Answer

Mathematics, 21.06.2019 17:30

For each proportion find the unknown number x 1/5/8=×/15

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

Select the sequences that are geometric.

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...