What the coefficient of 7x-6y+2

The weight of an organ in adult males has a bell-shaped distribution with a mean of 350 grams and a standard deviation of 45 gr

Svetach [21]

Answer:

a) About 68% of the data would be between 305 grams to 395 grams

b) About 95% of organs weighs between 260 grams and 440 grams

c)About 5% of organs weighs less than 260 grams or more than 440 grams

d) About 97% of organs weighs between 215 grams and 440 grams

Step-by-step explanation:

The empirical rule formula:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

(a) About 68% of organs will be between what weights?

We would be applying the First rule of the Empirical formula to this.

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

Mean = 350 grams

Standard deviation = 45 grams

Hence,

350 grams - 45 grams

= 305 grams

350grams + 45grams

= 395 grams

Therefore about 68% of the data would be between 305 grams to 395 grams

(b) What percentage of organs weighs between 260 grams and 440 grams?

Let try the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ - 2σ

= 350 - 2(45)

= 350 - 90

= 260

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Therefore, about 95% of organs weighs between 260 grams and 440 grams

(c) What percentage of organs weighs less than 260 grams or more than 440 grams?

Let try the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ + 2σ

= 350 - 2(45)

= 350 - 90

= 260

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Since, about 95% of organs weighs between 260 grams and 440 grams, the percentage of organs weighs less than 260 grams or more than 440 grams is calculated as:

100% - 95%

= 5%

Therefore, percentage of organs weighs less than 260 grams or more than 440 grams is 5%

(d) What percentage of organs weighs between 215 grams and 440 grams?

For 215 grams, we apply the 3rd rule to confirm

= 3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

Mean = 350 grams

Standard deviation = 45 grams

μ - 3σ

= 350 - 3(45)

= 350 - 135

= 215.

Hence, 99% of the organs weigh 215 grams

For 440, from the solve questions above, we know the second rule applies.

Hence,

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Hence,

99% + 95%/ 2

= 194% / 2

= 97%

Therefore, about 97% of organs weighs between 215 grams and 440 grams

4 0

4 years ago

What two whole number powers of 2 does 2 5/3 come between?

Whitepunk [10]

It
Wold be Yeas Bc fnfnfjzmmxmm ended dndnnsn was the best year to come pick ya girl up and get ready to get it gurl is a great night

5 0

3 years ago

You are given the polar curve r = e^θ

galina1969 [7]

The tangent to $r(\theta)=e^\theta$ has slope $\frac{\mathrm dy}{\mathrm dx}$ , where

$\begin{cases}x(\theta)=r(\theta)\cos\theta\\y(\theta)=r(\theta)=\sin\theta\end{cases}$

By the chain rule, we have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

and by the product rule,

$\dfrac{\mathrm dx}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\cos\theta-r(\theta)\sin\theta$

$\dfrac{\mathrm dy}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\sin\theta+r(\theta)\cos\theta$

so that with $\frac{\mathrm dr}{\mathrm d\theta}=e^\theta$ , we get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}=-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}$