Mathematics, 09.12.2019 23:31 kymberlyasher

Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 22 kg. what percentage of individual adult females have weights between 75 kg and 83 kg? if samples of 100 adult females are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are between 75 kg and 83 kg?

Answers: 1

Show answers

Answers

Answer from: aly95

14.28% of individual adult females have weights between 75 kg and 83 kg.

92.82% of the sample means are between 75 kg and 83 kg.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 22 kg. This means that $\mu = 79, \sigma = 22$ .

What percentage of individual adult females have weights between 75 kg and 83 kg?

This percentage is the pvalue of Z when X = 83 subtracted by the pvalue of Z when X = 75 . So:

X = 83

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

$Z = \frac{83 - 79}{22}$

Z = 0.18

Z = 0.18 has a pvalue of 0.5714.

X = 75

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

$Z = \frac{75- 79}{22}$

Z = -0.18

Z = -0.18 has a pvalue of 0.4286.

This means that 0.5714-0.4286 = 0.1428 = 14.28% of individual adult females have weights between 75 kg and 83 kg.

If samples of 100 adult females are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are between 75 kg and 83 kg?

Now we use the Central Limit THeorem, when n = 100 . So $s = \frac{22}{\sqrt{100}} = 2.2.$

X = 83

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

$Z = \frac{83 - 79}{2.2}$

Z = 1.8

Z = 1.8 has a pvalue of 0.9641.

X = 75

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

$Z = \frac{75-79}{2.2}$

Z = -1.8

Z = -1.8 has a pvalue of 0.0359.

This means that 0.9641-0.0359 = 0.9282 = 92.82% of the sample means are between 75 kg and 83 kg.

Answer from: Quest

da freeck kinda math is this just drop out

step-by-step explanation:

Answer from: Quest

hi there!

the answer will be d: 2

Another question on Mathematics

Mathematics, 21.06.2019 14:30

Two rigid transformations are used to map abc to qrs. the first is a translation of vertex b to vertex r. what is the second transformation? a reflection across the line containing ab a rotation about point b a reflection across the line containing cb a rotation about point c

Answers: 2

Answer

Mathematics, 22.06.2019 01:10

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).

Answers: 3

Answer

Mathematics, 22.06.2019 06:20

What is 2,489,287 divided by 7,482 to the nearest power.

Answers: 1

Answer

Mathematics, 22.06.2019 08:10

Raul works at a movie theatre. the function f(x) represents the amount of money raul earns per ticket, where x is the number of tickets he sells. the function g(x) represents the number of tickets raul sells per hour, where x is the number of hours he works. show all work to find f(g( and explain what f(g(x)) represents.

Answers: 1

Answer

You know the right answer?

Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard de...

Questions

Mathematics, 04.01.2022 17:40

If g(n) varies inversely with n and g(n)= 9 when n=4 then find the value of n when g(n)= 9 Round final answer to the tenths place.