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MAVERICK [17]
3 years ago
7

At a farm four employees harvest 48 pounds of food over a certain number of hours each employee works the number of hours shown

Mathematics
1 answer:
love history [14]3 years ago
7 0

Complete question :

At a farm, four employees harvest 48 pounds of food over a certain numbers of hours. Each employee works the numbered of hours shown. Employee A: 6 hours employee B: 4 hours employee C: 6 hours employee D: 8 hours The number of pounds of food harvested by each employee is proportional to the number of hours worked. Fill in the table with the amount of food, in pounds, each employee harvested.

Answer:

A = 12 lbs ;

B = 8 lbs

C = 12 lbs

D = 16 lbs

Step-by-step explanation:

Total hours worked :

(A + B + C + D)

(6 + 4 + 6 + 8) hours = 24 hours

Total pounds of food = 48 pounds

Pounds harvested per hour = 48 pounds / 24 hours = 2 pounds per hour

Amount of food harvested by each employee :

A = 6 * 2 = 12 pounds

B = 4 * 2 = 8 pounds

C = 6 * 2 = 12 pounds

D = 8 * 2 = 16 pounds

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Answer:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (2)  

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got z_{\alpha/2}=1.96, replacing into formula (2) we got:  

n=(\frac{1.96(0.25)}{0.1})^2 =24.01  

So the answer for this case would be n=25 rounded up to the nearest integer  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)  

\sigma=0.25 represent the population standard deviation

n represent the sample size (variable of interest)  

Solution to the problem

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}  

The margin of error is given by this formula:  

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

And on this case we have that ME =0.1 and we are interested in order to find the value of n, if we solve n from equation (1) we got:  

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (2)  

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got z_{\alpha/2}=1.96, replacing into formula (2) we got:  

n=(\frac{1.96(0.25)}{0.1})^2 =24.01  

So the answer for this case would be n=25 rounded up to the nearest integer  

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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