3.2.31 The weight of an organ in adult males has a bell-shaped distribution with a mean of 320 grams and a standard deviation of 20 grams. Us

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

(b) What percentage of organs weighs between 280 grams and 360 grams?

(c) What percentage of organs weighs less than 280 grams or more than 360 grams?

(d) What percentage of organs weighs between 300 grams and 360 grams?

This question is incomplete

Complete Question

The weight of an organ in adult males has a bell shaped distribution with a mean of 320 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following. A.) About 68% of organs will be between what weights? B.) what percentage of organs weighs between 280 grams and 360 grams? C.) what percentage of organs weighs less than 280 grams or more than 360 grams? D.) what percentage of organs weighs between 300 grams and 360 grams?

A.) About 68% of organs will be between what weights?

Therefore, 68% of the organs will weigh between 300 and 340 grams.

B.) what percentage of organs weighs between 280 grams and 360 grams?

95%

C.) what percentage of organs weighs less than 280 grams or more than 360 grams?

5%

D.) what percentage of organs weighs between 300 grams and 360 grams?

81.5%

Step-by-step explanation:

Empirical formula states that:

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

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

Where:

μ = Population mean

σ = Population standard deviation

From the above question, we have the following information

Mean weight = 320 grams

Standard deviation = 20 grams

a) About 68% of organs weight between:

To solve for this, we would use the empirical rule:

68% of the data values lie within 1 standard deviation of the mean

Hence, 68% of the data values lie in the range:

Mean - 1 standard deviation to Mean + 1 Standard Deviation.

Mean - 1 Standard Deviation

μ - σ

= 320grams - 20grams = 300 grams

Mean + 1 Standard Deviation

μ + σ

= 320grams + 20grams = 340 grams

Therefore, 68% of the organs will weigh between 300 and 340 grams.

B.) what percentage of organs weighs between 280 grams and 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 280 grams - 320 grams = -40 grams

x - mean = 360 grams - 320 grams = 40 grams

Note that both differences = 2 × standard deviation

Hence, from the empirical formula above,

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

Therefore, 95% of the organs fall between 280 grams and 320 grams

C.) what percentage of organs weighs less than 280 grams or more than 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 280 grams - 320 grams = -40 grams

x - mean = 360 grams - 320 grams = 40 grams

So, from the empirical formula above,

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

Therefore, 95% of the organs fall between 280 grams and 320 grams

It is important to note that finding the percentage of data that weighs less than or more than the given range of values, the formula is given as:

Percentage of Value outside( less than or more than) the range = 100% - Percentage of values within the range

100% - 95%

= 5%

Therefore, the percentage of organs weighs less than 280 grams or more than 360 grams is 5%

D.) what percentage of organs weighs between 300 grams and 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 300 grams - 320 grams = -20 grams

20 grams = 1 × standard deviation

For 300 grams, the empirical formula that states that:

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

It is important to note that the percentage of values below the mean and above the mean must be the same.

But since this is a bell shaped distribution, the percentage of data between 300 and 320 grams = 68%/2

= 34%

x - mean = 360 grams - 320 grams = 40 grams

40 = 2 × standard deviation

For 360 grams , the empirical formula that states that,

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

It is important to note that the percentage of values below the mean and above the mean must be the same.

Since this is a bell shaped distribution, the percentage between 320 and 360grams = 95%/2

= 47.5%

Therefore, the percentage of organs that weighs between 300 grams - 360 grams = 34% + 47.5%

= 81.5%

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

i think it would be 42cm